Geometry in Nature and in Art Day 2 (8/21/2012) Objectives: Use geometry to create art designs. Identify reflectional and rotational symmetry. Assignment

Geometry in Nature and in Art

Day 2 (8/21/2012)

Objectives:• Use geometry to create art

designs. • Identify reflectional and

rotational symmetry.

Assignment

Class work • Decorate the folder using

designs on page 8,10, 11, and 35*

• Identify reflectional or rotational symmetry of your design.

• Homework Read lesson 1.1 Page 28

Section 1.1 Building blocks of Geometry

Day 3 (8/22/2012)

Objectives: • Learn the terminology and

the notation of points, lines, segments, rays, plane, collinear and coplanar points.

Assignment

Class Work • Finish the Folder design. (15

min)• Take notes from the LCD on

definitions. Work on the Investigation

on page 32. Homework Page 33 # 1-15 all

Section 1.1 Building blocks of Geometry

Day 4 (8/23/2012)

Objectives: • Learn the terminology and

the notation of points, lines, segments, rays, plane, collinear and coplanar points.

Assignment

Class Work • Go over homework

questions. Homework Page 34 # 18-35 all

Warm-up Day 4

Graph each point:• A(0,-2), B(-1,2), C (3,0), D(-1,-3)Graph and name:1. The line that passes through A and B.2. The line segment that passes through D and

C.3. The ray with initial point C and passes

through A.

Section 1.1 Midpoint

Day 5 (8/24/2012)

Objectives:• Review coordinate midpoint

property. • Find the coordinates of the

midpoint by using midpoint formula.

Assignment

Class work • Warm-up (5 min)• LCD Power Point

presentation. • Page 37 # 1-8 allHomework:• Read section 1.2 Page 38.

Section 1.2 Poolroom Math

Day 6 (8/28/2012)

Objectives:• Definition of a angle.• Learn how to show the

measure of an angle. • Become familiar with the

symbols of marking angles and congruent angles.

Assignment

Class Work • LCD lectures• Go over Examples B and C

page 40-41.• Go over page 42-43 # 1, 2,

15, 16, 20.HomeworkPage 42-43 # 1-25 all.

Section 1.2 Poolroom Math

Day 7 (8/29/2012)• Objectives:• Definition of a angle.• Learn how to show the

measure of an angle. • Become familiar with the

symbols of marking angles and congruent angles.

Assignment Class Work:Collect homework day 4.• Page 44-45 # 31-40 all.Homework :• Review Concept and

notation of sections 1.1-1.2.

Warm- up Day 7 1. Find the coordinates of the midpoint of the segment with the given

endpoints (5,8) and (3, 2).

2. Tell whether the statement below is sometimes, always, or never true. Support your answer with a sketch.If M is the midpoint of KL, then M, K, and L are collinear.

Definition: Angle Bisector

• An angle bisector is a ray that divides an angle into two congruent angles.

• JK bisects LJM; thus LJK KJM.

Example 1

• KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

Example 1 Continued

• Step 1 Find x.

mJKM = mMKL

(4x + 6)° = (7x – 12)°

+12 +12

4x + 18 = 7x

–4x –4x

18 = 3x

6 = x

Def. of bisector

Substitute the given values.

Add 12 to both sides.

Simplify.

Subtract 4x from both sides.

Divide both sides by 3.

Example 1 Continued

• Step 2 Find mJKM.

mJKM = 4x + 6

= 4(6) + 6

= 30 Substitute 6 for x.

Simplify.

Quiz

Day 8 (8/30/2012)• Objectives:• Quiz on section 1.1-1.2

Assignment • Homework • Read section 1.3

Section 1.2

Day 8 (8/30/2012)• Objectives:• Understand the definition of

angle bisector.• Use the definition of the

angle bisector to find the missing side.

Assignment Class Work Go over the warm up. Quiz (30 min )HomeworkRead section 1.3

Section 1.3

Day 9 (8/31/2012)• Objectives:• Review section 1.1-1.2

concepts. • Practice to write definitions. • Define special angle

relationship.

Assignment Class work • Go over the worm up• Go over the quiz • Go over example B on page

48. • Go over the investigation on

page 49. Homework Learn the definitions of special

angles.

Warm- up Day 9 (8/31/2012)

• 1. Copy the figure. Write what you know about the markings.

R

P

Q

N

M

Warm up

1. Find the measure of each angle.

QS bisects PQR, mPQS = (5y – 1)°, andmPQR = (8y + 12)°. Find mPQS.

2. JK bisects LJM, mLJK = (-10x + 3)°, andmKJM = (–x + 21)°. Find mLJM.

Section 1.3

Day 10 (9/4/2012)• Objectives:• Practice to write definitions. • Define special angle

relationship.

Assignment Class Work • Go over the warm up. • Go over investigation

“ Definition of angles” on page 49.

Homework Page 51 -52 # 1-8 all, 11, 13.

Warm-up Day 10

1. E is between D and F. Find DF.

2. D is the midpoint of EF, ED = 4x + 6, and DF = 7x – 9. Find ED, DF, and EF.

E4x + 6 D 7x – 9 F

Section 1.3

Day 11 (9/5/2012)Objectives:Use the definition of special

angles to find the missing angle or solve for X.

Assignment Class Work • Go over the Warm up• Go over the homework. • Go over examples from the

hand out. Homework • Finish the hand out

Warm up Day 11

• mA = 60, and mB =70. Find the measure of each of the following.

• 1. supplement of A

• 2. complement of B

• 3. Determine whether this statement is true or false. If false, explain why. If two angles are complementary and congruent, then the measure of each is 90°.

•

Section 1.3 Special angels

Day 12 (9/ 6/ 2012)Objectives:• Review sections 1.1-1.3

Assignment Class Work • Go over the Warm up• Go over examples from the

Hand out. Homework • Finish the hand out and

review for the quiz.

Warm up Day 12 1.

Name the pairs of vertical angles.

2. mXYZ = 2x° and mPQR = (8x - 20)°.

If XYZ and PQR are supplementary, find the measure of each angle.

Answers to the homework of Day 11• 2. 70/3• 3. x = 10 and m<ABC = 52• 8. x = 30 and m<AOB = 30• 9. x = 30 and m< BOC = 120• 10. x = 20 and m< BOC = 40• 11. x = 8• 12. y = 35• 13. 35• 14. LM= 20, MN = 3 • 15. m< COB = 61, m< BOA = 29

Quiz on Sections 1.1-1.3

Day 13 (9/7/2012)

• Objectives: • Test concepts of sections

1.1-1.3.

Assignment Class Work • Finish the Review hand out. • Quiz Homework: • Read section 1.4 page 54-

55.

Section 1.4 Polygons

Day 14 (9/10/12)Objectives:• Define and classify polygons

and related terms. • Practice writing definitions. • Learn even more

vocabulary.

Assignment Class WorkGo over the warm up. • Go over the vocabulary of

section 1.4.• Homework • Page 57 # 1-12 all 15, 21,

22.

Day 14 Warm up

Identify each of the following.• 1. points that lie in the same plane • 2. Two angles whose sum is 180°• 3. Two lines that never meet. • 4. An angle that is less than 90 degree.

Day 14 Vocabulary

1. Polygon2. Diagonal 3. Convex4. Concave5. Congruent polygons6. Perimeter7. Equilateral Polygon 8. Equiangular Polygon 9. Regular Polygon

Vocabulary Day 14 1. Polygon • A polygon is a closed figure, formed by connecting line segments endpoint to

endpoint with each segment intersecting exactly two others.

2. Diagonal • Diagonal of a polygon is a line segment that connects two nonconsecutive vertices.

3. Convex Polygon • A polygon is convex if no diagonal is outside of the polygon .

4. Concave Polygon • A polygon is concave if at least one diagonal is outside of the polygon.

5. Congruent Polygons• If polygons are congruent, then corresponding sides and angles are congruent

OR

If corresponding sides and angles are congruent, then the polygons are congruent.

6. Perimeter

The perimeter of a polygon is equal to the sum of the lengths of its sides.

Vocabulary Continues….. 7. Equilateral Polygon

• Equilateral polygons are polygons in which all sides have equal length. 8.Equiangular Polygons • Equiangular polygons are polygons in which all angles have equal

measure.

9. Regular Polygons• Regular polygons are polygons that are both equilateral and equiangular.


Day 15 (9/11/2012)

Objectives:• Define and classify polygons

and related terms. • Practice writing definitions. • Learn even more vocabulary

Assignment Class WorkCollect Homework day 14.• Go over the warm- up• Go over the quiz.

Homework • Page 58 23-25 all.

Day 15 Warm up Classify each angle as acute, obtuse, or right.

• 1. 2.

• 3.

4. If the perimeter is 47, find x and the lengths of the three sides.


Day 16 9/12/2012Objectives:• Test concepts of sections.

1.1-1.4

Assignment Class Work • Quiz make up • Hand-out. Homework Finish the hand-out


Day 17 9/13/2012

Objectives:• Review definition of a

polygon and related terms. • Use the definition to solve

problems.

Assignment Class Work • Go over the warm up.• Go over the homework

questions.• Finish the hand-out.Homework Read section 1.5 find a

definition and write an example for each bolded term.

Section 1.5 Triangles

Day 18 (9/14/2012)Objectives:• Define and classify triangles • Practice with definitions.

Assignment Class work Go over the warm up • Go over the homework

questions. • Note book quiz. Homework Page 62 # 1-9 all, page 63 17-

21 all.

Warm up day 18

Define the following terms. 1. Right triangle

2. Equilateral triangle

3. Obtuse triangle

4. Collinear Points

Vocabulary Day 18 Right triangle • A right triangle has a right angle.

Acute triangle• An acute triangle has three acute angles

Obtuse triangle • An obtuse triangle has one obtuse angle.

Scalene triangle• A scalene triangle is a triangle with no congruent sides.

Equilateral triangle • An equilateral triangle has three congruent sides.

Isosceles triangle.• An isosceles triangle has at least two congruent sides.

Section 1.5 Triangles

Day 19 (9/18/2012)• Objectives:• Define and classify triangles • Practice with definitions. • Use the definitions of

sections 1.2-1.5 to answer hand out questions.

Assignment Class Work 1. Go over the Warm up.2. Go over homework

Questions.3. Hand out 1-9 AllHomework Defined the bolded terms on

section 1.6

Warm up Day 19 1. Classify EHF by its side lengths.

2. Find the side lengths of equilateral FGH.

Warm up Day 20

• Classify each triangle by its angles and sides.

• 1. MNQ

• 2. NQP

• 3. MNP

Warm up Day 20

Answers • Classify each triangle by its angles and sides.

• 1. MNQ

• 2. NQP

• 3. MNP

acute; equilateral

obtuse; scalene

acute; scalene

Section 1.6 Special Quadrilaterals.

Day 20 (9/19/2012)

Objectives:• Define and classify

quadrilaterals along with their related parts.

• Learn more vocabulary related to quadrilaterals.

Assignment Class Work • Go over the warm up • Go over homework

questions. • Write definitions of the

bolded terms. Homework • Page 66 # 1-13 all.

Vocabulary Day 20 1. Trapezoid • A trapezoid is a quadrilateral with exactly one pair or parallel sides. 2. Kite • A kite is a quadrilateral with two distinct pair of consecutive congruent

sides. 3. Parallelogram • A parallelogram is a quadrilateral with two pairs of parallel sides. 4. Rhombus • A rhombus is an equilateral parallelogram 5. Rectangle • A rectangle is a equiangular parallelogram. 6. Square A square is a regular quadrilateral .

Section 1.7 Special Quadrilaterals.

Day 21 (9/20/2012)

Objectives:• Learn more vocabulary

related to quadrilaterals• Use the definitions of this

section to solve problems.

Assignment Class Work • Go over the warm up. • Collect Homework day 20.• 30 min Quiz on section 1.6-

1.7. Homework • Hand out page 6.

Warm up Day 21

For 1-3 , draw and label each figure. 1. An obtuse triangle ABC with obtuse angle <A. 2. An isosceles right triangle KLM with KL=KM

and m<K=90. 3. A Kite ABCD with AB=3cm, BC=3cm, CD=6

cm, and AD= 6 cm. 4. If KL=5 in, what is the perimeter of a regular

polygon KLMNP.

Section 1.7 Circles

Day 22 (9/21/2012)Objectives:• Define a circle and related

figures. • Identify parts of a circle.

Assignment Class Work 1. Go over the warm up 2. Defined the circle and

parts of a circle. 3. Start working on the

homework Homework:Page 72 # 2-9 all, 11, 23-26 all.

29, 30, 34.

Warm up Day 22

1. Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.

Vocabulary of section 1.7

1. Circle • A circle is a set of points equidistant from a fixed point called

the center. 2. Chord• A chord is a line segment whose end points lie on the circle.3. Diameter • A diameter is a chord that passes through the center. The

diameter is the longest cord. 4. Tangent • A tangent is a line that intersects the circle only once.

Vocabulary 1.7….5. Arc • An arc is made of two points on the circle and the continuous (unbroken)

part of a circle between the two points. The two points are called the end points.

6. Semicircle• Is the arc of the circle whose endpoints are the end points of a diameter. 7. Minor Arc• A minor arc is an arc that is smaller than a semicircle. 8. Major Arc • A major arc is a arc that is larger than the semicircle. Central angle • A angle whose vertex is the center of a circle.

Example 1.

• Identify each term.

Chords:

Semicircle

Tangent:

Diameter:

Radius:

Minor arc:

Major arc:

Section 1.8 Space Geometry

Day 23 (9/24/ 2012)

Objectives:• Visualize Objects and

relationships in two and three dimension.

• Practice drawing skills

Assignment Class Work• Go over the warm up.• Go over the homework

questions. • Practice drawing important

geometric solids. Homework Page 78 1-6 all and 14-17 all.

Day 24 9/25/2012

• No school Teacher’s Planning Day

Warm up Day 23 • Definition: “The measure of an arc is equal to the measure of the

corresponding central angle”. • Use the definition to find the measure of each given arc. Name the arc.

180o

D

130o

50o

C

A

B

Em AB=

m BC=

m AEC=

m BCA=(

((

(

Chapter 1 Review

Day 25 (9/27/2012)Objectives:• Review vocabulary and

notation of chapter 1.• Use concepts of this chapter

to solve word problems.

Assignment Class work • Go over the warm up. • Go over page 91 # 31, page

92 # 32, 41, 43, 46.• Collect homework Day 23. Class work / Homework • Page 90, 1-25 all, 26, 39, 40,

42,44.

Day 26 9/28/2012

• Chapter 1 Test

Warm up Day 25

Tell whether each statement is true or false. • A Rhombus is a quadrilateral that has exactly one pair

of parallel sides. • “The ray from point L to point M” is called LM.• The vertex of angle RST is the point T.• A diagonal is a line segment in a polygon connecting

any two vertices.

Sections 2.1-2.2 Inductive Reasoning

Day 27 10/ 1/ 2012Objectives:• Introduction to inductive

Reasoning. • Use the inductive reasoning

to find the next term.

Assignment Class Work • Define the bolded terms. • Work investigation on page

98 and problems 5 and 8.• Work on investigation on

page 102 and example A on page 103.

Homework Page 99 # 3, 7, 17.Page 105 #

1,2,3,4.

Section 2.4 Deductive Reasoning

Day 28 (10/2/2012)

Objectives: • Introduction to deductive

Reasoning. • Learn the relationship

between inductive and deductive reasoning.

Assignment Class Work • Go over the warm up.• Write the definition of

deductive reasoning.• Work on Example B on page

115 and investigation “Overlapping Segments on Page 116.

• Start the homework. HomeworkPage 117 1-5 all,8.

Day 28 Warm up • Identifying a Pattern1. Find the next item in the pattern.January, March, May, ... 2. Find the next item in the pattern.7, 14, 21, 28, …3. Find the next item in the pattern

Section 2.5 Angle Relationships

Day 29 (10/3/2012)Objectives: • Discover relationship

between special pairs of angles.

• Practicing performing investigations and writing conjectures.

Assignment Class Work • Go over the warm up.• Work on investigations 1

and 2. on page 122-123. • Page 124 # 1-4 all and page

118 # 14-16 all, 22-31 all, and 33, 35. Due in the end of the class.

Day 29 warm up

Is the conclusion a result of inductive or deductive reasoning?

1. At Reagan High School, students must pass Geometry before they take Algebra 2. Emily is in Algebra 2, so she must have passed Geometry.

Section 2.5 Angle Relationships

Day 30 (10/4/2012)Objectives: • Discover relationship

between special pairs of angles.

• Note book Quiz

Assignment Class Work• Go over the warm up.• Work on problems page 125

# 5, 8, 9, 10, 11, 13, 15. • Note book Quiz.

Section 2.6 Special Angles and Parallel Lines.

Day 31 (10/5/2012)

Objectives: • Explore relationship of the

angles formed by a transversal cutting parallel lines .

• Complete the conjectures on page 129.

Assignment Class Work Note book Quiz Homework : Define the Bolded terms on

page 128.Work on investigation 1 on

page 128 and complete the conjectures on page 129.

Day 28 Warm up Answers

1. The next month is July. 2. Multiples of 7 make up the pattern. The next

item is 35. 3. In this pattern, the figure rotates 90° counter-

clockwise each time. The next figure is .

Section 2.6 Special Angles and Parallel Lines.

Day 32 10/8/2012Objectives: • Explore relationship of the

angles formed by a transversal cutting parallel lines .

• Complete the conjectures on page 129.

Assignment Class Work • Go over the warm up • Complete the conjectures

on page 129. • Start the homework Homework Page 131-133# 1,2, 3, 6,7, 9, 10,14, 15, 16.

Day 32 (10/8/2012) Warm up

• mXYZ = 2x° and mPQR = (8x - 20)°.

1. If XYZ and PQR are supplementary, find the measure of each angle.

2. If XYZ and PQR are complementary, find the measure of each angle.

3. If <XYZ and < PQR are vertical, find the measure of each angle.

Chapter 2 Review

Day 33 10/9/2012Objectives: • Review and apply concepts:• Deductive reasoning• Inductive reasoning.• Vertical and linear pair if

angles. • Special Angles on parallel

lines.

Assignment Class Work • Go over the warm up • Go over homework

questions. Homework Page 140 # 4, 6, 7, 15, 19.

Day 33 Warm up

• 1.Find m< ECF.• 2. Find m<DCE.

Homework Answers Day 10/8/2012

• 1 63 • 2 90• 3 No• 6 113• 7 a=d=64, b=c=116, e=g=i=j=k=108, f=h=s=72,

m=105, n=79, p=90, q=116, t=119.

• 9 56 + 114 = 170 NO 180 • 10 55 + 45 = 100 no 180 • 14 42• 15 20• 16 The lines are not parallel

Chapter 2 Review Day 34 10/10/2012Objectives: • Review and apply concepts:• Deductive reasoning• Inductive reasoning.• Vertical and linear pair if

angles. • Special Angles on parallel

lines.

Assignment Class Work Go over examples from the

hand out. Go over questions from the

hand out. Homework Finish the Hand out

Day 34 Warm up

Day 35 10/11/2012

Chapter 2 Test

Algebra Review

Day 36 10/12/2012Objectives:• Review evaluating

expressions and solving linear equations.

Assignment Class Work • Go over the warm up • Go over examples from the

hand out. • Finish the hand out

Day 36 Warm up

• Find mABD.

Section 3.1 Duplicating Segments and Angles

Day 37 10/15/ 2012Objectives:• Distinguish among

construction, Sketch, and drawings of geometry figures.

• Discover constricting methods to duplicate a segment , an angle, and a polygon.

Assignment Class Work • Go over the warm up. • Do vocabulary of section

3.1.• Follow the steps of the

hand out and complete each construction on examples 1-5.

Homework Page 147 # 1,2 ,4, and 7

Day 37 Warm up

Solve for x. 1. 2x- 4+ 3x = 62. -5x -10 = 20x 3. -3x – 2 –x = 6

Vocabulary of Section 3.1

1. Sketch When we sketch a geometric figure ( for example a equilateral

triangle) we make a freehand figure ( equilateral triangle)2. Draw When we draw a geometric figure ( an equilateral triangle), we use a

protractor to measure the angles and a ruler to measure the sides.

3. Construct When we construct a geometric figure, we use a straightedge and a

compass only. 4. Duplicate Means to copy a figure using straightedge and compass only.

Section 3.2 Construction Perpendicular Bisectors

Day 38 10/16/2012

Objectives:• Construct perpendicular

bisectors and midpoints. • Make conjectures about

perpendicular bisectors.

Assignment Class Work • Go over the warm up • Do the vocabulary of

section 3.2.• Follow the steps of the

video and complete each construction.

Homework Finish the hand out

Day 38 Warm up

• Find the midpoint of the segment with the given endpoints.

• 2. (–1, 6) and (3, 0)

• 3. (–7, 2) and (–3, –8)

Vocabulary of Section 3.21.Segment bisector • A segment bisector is a ray, a line, or a segment that passes

through the midpoint. 2.Perpendicular bisector A perpendicular bisector is a line, segment , or ray that is

perpendicular to a segment at its midpoint.3.Median Median is a segment that connects the vertex of a triangle with

the midpoint of the opposite side. 4.MidsegmentA segment that connects the midpoints of two sides of a triangle

is called the midsegment.

Section 3.3-3.5 Constructing Perpendiculars to Lines.

Day 39 10/17/2012

Objectives:• Constructing perpendiculars

to a line. • Construct the altitudes of a

triangle. • “PAST Testing this lecture

moved for Friday “

Assignment

Class Work • Go over the warm up • Do the vocabulary of section

3.3.• Sketch a triangle and draw

the altitude from every angle.• Solve the three problems

written on the board. Homework Page 153 # 15-20 all

Section 3.3-3.5 Review

Day 40 10/18/2012Objectives:Review:• Special angle and parallel

lines. • Vertical angles • Constructing with simple

geometric tools.

Assignment Class Work Notebook Quiz

Section 3.3-3.5 Constructing Perpendiculars to Lines.

Day 41 10/19/2012Objectives:• Constructing perpendiculars

to a line. • Construct the altitudes of a

triangle.

Assignment Class Work 1. Go over the warm up 2. Do the vocabulary of section

3.3.3. Solve the three problems

written on the board.

4. Class work is due in the end of the class.

Homework Page 153 # 15-20 all

Day 41 Warm Up

• Refer to the diagram. Use the given information and the theorems you have learned to show that r || s.

m3 = 2x, m7 = (x + 50), x = 50

Vocabulary 3.3

1.Distance from a line.• Distance from a point to a line is the length of the

perpendicular segment from the point to the line. 2.Altitude • An a altitude of a triangle is a perpendicular segment

from the vertex to the opposite side. 3.Orthocenter • Orthocenter is the point where the three altitudes of a

triangle meet. The three altitudes of a triangle are congruent(have the some length ) .

Section 3.5 Constructing Parallel Lines Day 42 10/22/2012Objectives:• Construct parallel lines

using compass and straightedge .

• Find the slope of a lines. • Parallel and perpendicular

lines and their slopes.

Assignment Class Work • Hand out

Section 4.1 Triangle Sum Conjecture

Day 43 10/23/2012Objectives:• Use triangle sum theorem . • Develop inductive and

deductive reasoning.

Assignment Class work• Go over the warm up.• Use triangle sum conjecture

to solve problems. • Start working on the hand

out. # 1-13 all.Homework • Finish the hand out

Triangle Sun Conjecture or Theorem

Day 43 Warm up

• For the given triangle sketch the altitude from <C and labeled CK . Sketch the median from <B and labeled BN

•

B

AC

Day 44 Warm up

1. Find the Measure of the indicted angle.

Review Parallel lines and Triangle Sum Conjecture

Day 45 10/25/2012 Assignment

Class Work • Hand out

Objectives:Review angle relationship of

two parallel lines and a transversal.

Review triangle sum conjecture.

• (Early Release Day )

Day 46 10/26/2012

• No School Teachers Planning Day

Section 4.2 Properties of Isosceles Triangles

Day 47 10/29/2012Objectives:• Discover the relationship

between the base angles of an isosceles triangle.

• Learn new vocabulary • Construct points of

concurrency of the given triangle.

(Block schedule day 48 10/30/2012)

Assignment Class Work • Go over the warm up • Go over the properties of

isosceles triangle. • Go over problems from the

hand out. • Finish the hand out.• “Due in the end of the

class!”

Properties of Isosceles Triangle • 1.If a triangle is isosceles, then its base angles

are congruent. • 2. If two base angles of a triangle are

congruent, then the triangle is isosceles.

Leg Leg

Base

__ __

More vocabulary 1. When a set of lines have a point in common they are concurrent. 2. The Angle Bisector Conjecture • The three angle bisectors of a triangle meet at a point (are

concurrent).This point is called the incenter. 3. The Perpendicular Bisector Conjecture • The three perpendicular bisectors of a triangle meet at a point

called circumcenter.4. The Altitude Conjecture • The three altitudes of a triangle meet at a point (are concurrent

) called the orthocenter. 5. The point of intersection (concurrency) of the three medians is

called the centroid.

Interim Review Day 49 10/ 31/2012Objectives:• Review concepts of

chapters 1-3. • Prepare for the interim

Assessment .• (Block Schedule day 50

11/1/2012)

Assignment Class Work Go over the warm up. • Hand out • 40 min independent work. • Go over questions and

unsolved problems.

Day 51 11/2/2012

Interim Assessment

Day 52 11/5/2012Interim Assessment

DAY 53 11/6/2012 No school teachers planning day

Section 4.3 Triangle Inequalities

Day 54 11/7/2012Objectives: • Investigate the relation

among sides and angles of a triangle.

• Exterior Angle Conjecture.•

Assignment Class Work • Go over the warm up • Go over the conjectures.Class Work/ Homework Page 218 # 1-9 all and #

14,15,16.

Section 4.3 Conjectures

1. Triangle Inequality Conjecture The sum of the lengths of any two sides of a triangle is greater

than the length of the third side triangles.

2.Side-angle Inequality The angle opposite the longest side is the largest angle.

3.Exterior angle conjecture The measure of the exterior angle of a triangle is equal to the

sum of the measure of the remote interior angles.

Day 54 Homework Answers

• 5) a,b,c• 6) c,b,a • 7) b,a,c• 8) a,c,d• 9) a,b,c • 14) 135• 15 ) 72• 16) 72

Section 4.3 Triangle Inequalities

Day 55 11/8/2012Objectives: • Investigate the relation

among sides and angles of a triangle.

• Exterior Angle Conjecture.•

Assignment Class Work Go over the Warm up Go over problems from the

hand out Finish the hand out

Section 4.4 Are there Congruence Shortcuts.

Day 56 11/9/2012Objectives:• Explore shortcut methods

of determining whether triangles are congruent.

• Types of triangle congruency.

Assignment Class Work • Go over the warm up • Go over SSS and SAS

conjecture.• Go over Examples.Homework Page 224 # 4-9 all 12, 13, 16.


Section 4.5 Congruence Shortcuts

Day 57 11/13/2012

Objectives:• Explore shortcut methods

of determining whether triangles are congruent.

• Types of triangle congruency.

Assignment Class Work • Go over the warm up • Go over ASA, SAA,

congruencies. • Start with the Homework Homework • Page 229 # 4-9 all. 10,12,

14, 16, 18.

Angle-Side-Angle Congruence

Angle-Angle-Side Congruence

Review Sections 4.3-4.4 Day 58 11/14/2012

Objectives:• Review triangle congruence. • Practice SAS, SAA, ASA,SSS.

Assignment Class Work • Go over homework

questions. • Go over problems from the

hand out. • Hand out due in the end of

the class********

Section 4.6 Corresponding Parts of Congruent Triangles

Day 59 11/15/2012Objectives:Show that pairs of angles or

pairs of sides by identifying related triangles and proving them congruent.

Assignment Class Work Go over the warm up.Go over the definition of

congruence. Go over proving triangle

congruence. Homework Page 233 # 1, 2, 3, 4, 5, 7, 9

Day 60 11/16/2012

Notebook Quiz Chapter 3 and 4.1-4.6

Section 4.6 Corresponding Parts of Congruent Triangles

Day 61 11/19/2012Objectives:Show that pairs of angles or


Assignment Class Work Go over the warm up. Go over proving triangle

congruence. Go over # 1, 12, 15. Finish the Hand out.

Day 62 11/20/2012

• The class will be in the Lab

Day 63 11/21/2012

Sections 4.1-4.6 Quiz

Sections 4.1-4.5 Review

Day 64 1/26/20122

Objectives: Show that pairs of angles or


• Investigate the relation among sides and angles of a triangle.

• Exterior Angle Conjecture.

Assignment Class Work Go over the Quiz Homework Quiz Corrections

Section 4.7 Flowchart Thinking

Day 65 11/28/2012Objectives: • Create flowchart proofs. • Develop problem solving

skills. • Develop Logical and visual

thinking.

Assignment Class Work• Go over the warm up. • Go over Examples A and B

on page 237-238. Page 239 # 2

Homework Page 240 # 3,4,5,8,10.

Section 4.8 Proving Special Triangle Conjecture

Day 66 11/29/2012 Objectives:• Practice Writing flow charts.• Investigate vertex and angle

bisector of isosceles triangle.

• Use properties of Isosceles triangle to find properties of equilateral Triangle.

Assignment Class Work Go over the warm up.Go over homework questions.Homework Study the homework Pop Quiz

tomorrow.


Day 67 11/29/2012 Objectives: Review and practice flow

charts and properties of isosceles and equilateral triangles .

Assignment Class Work Go over the Warm up Go over questions from the

Hand out.

Chapter 4 Review

Day 68 12/ 3/2012 Objectives:• Show that pairs of angles or



• Exterior Angle Conjecture.• Investigate vertex and angle


Assignment Class Work Go over the warm up. Go over problems from the

Hand out. Page 252, Work on problems

7-18 all, 29, 32.

Day 69 12/4/2012

• The class is in the Lab• Working on sections 1.1-1.5.

Chapter 4 Review

Day 70 12/5/2012Objectives:• Show that pairs of angles or



• Exterior Angle Conjecture.• Investigate vertex and angle


Assignment Class workGo over the warm up. Go over problems from the

Hand out.# 19-26 all.27*,28,29, 32.

Day 70 12/6/2012

Chapter 4 Test

Section 5.1 Polygon Sum Conjecture

Day 71 12/7/2012Objectives: Discover the sum of the angle

measures in a polygon. Practice construction skills.Develop reasoning.

Assignment Class Work:Go over the warm up.Go over Investigation 1. and

problem # 5 and 8. Start working on the

homework. Homework Page 259 # 1, 2, 3, 4, and 7.

Section 5.1 Polygon Sum Conjecture

Day 73 12/11/2012 Objectives: Discover the sum of the angle


Assignment Class Work:Go over the warm up.Page 260 # 9,10,13,14. Yesterday’s Homework Pg 260 # 5, 6, 8, 12 DUE IN THE END OF THE

CLASS.

Section 5.2 Exterior angles of a Polygon

Day 77 12/14/2012

Objectives:• Discover the sum of the

measures of the exterior angles of a polygon.

• Use the formula for the measures of the exterior angles of a polygon.

Assignment Class Work• Go over the warm up. • Write the Exterior Angle

Conjecture. • Start working on the

homework # 1,2,3,7. Homework:Page 263 # 1-9 all. Make up work page 252 #7-24

all,27 and 29.

Section 5.1-5.2 Practice

Day 75 12/12/2012 Objectives: Discover the sum of the angle


Assignment Hand-out .Due in the end of the class.

Section 5.2 Exterior angles of a Polygon

Day 76 12/13/2012Objectives:• Review concepts of sections

5.1-5.2. • Early release day

Assignment Class Work • Finish problems 1-3

Section 5.3 Kite and Trapezoid Properties.

Day 77 12/17/2012 Objectives:• Discover the properties of

kites and Trapezoids .• Learn more vocabulary

Assignment Class Work • Go over the warm up • Complete the vocabulary of

section 5.3.Homework Page 271 # 1-4 all.

Lab Practice

Day 78 12/18/2012Objectives: Plan A Review Chapters 2-3

Concepts. Plan B If the program does not work Finish Monday's homework

Assignment Class Work • Log in cognitive tutoring

and work on assigned sections.

Section 5.4 Properties of Midsegments

Day 79 12/19/2012 Objectives:• Define and discover

properties of the midsegment in a triangle and trapezoid.

• Practice constructions skills.

Assignment Class Work • Go over the warm up• Write section 5.4

conjectures. Homework Page 277 # 1-8 all.


Day 80 12/20/2012 Objectives:Review properties of the Kite,

Trapezoids , and midsegments.

Assignment Class Work • Hand out • Section 5.3 # 1-5.• Section 5.4 # 1-5.“Due in the end of the class”

Day 81 12/21/2012

Note book Quiz

Section 5.5 Properties of a Parallelogram.

Day 82 1/7/2013Objectives:• Review the definition on a

parallelogram.• Discover properties of the

parallelogram. • Write conjectures this

section.

Assignment Class Work • Go over the warm up• Complete conjectures of

section 5.5. • Start working on the

homework Homework: Page 283 # 1-6 all, 16.

Section 5.5 Parallelogram Conjectures

1. The opposite angles of a parallelogram are congruent.

2. The consecutive angles of a parallelogram are supplementary.

3. The opposite sides of a parallelogram are congruent.

4. The diagonals of a parallelogram bisect each other.

Section 5.6 Properties of Special Parallelograms.

Day 83 1/8/2013 Objectives: • Discover the properties of

Rhombus, Rectangle, and Square.

• Write the conjectures of this section.

Assignment Class WorkGo over the warm up Go over the conjectures of this

section. Start with the homework HomeworkPage 294 # 1-13 odd.


1. Definition . A rhombus is a parallelogram with four

congruent sidesRhombus conjectures:1. The diagonals of a rhombus are

perpendicular and bisect each other. 2. The diagonals of e rhombus bisect the angles

of the rhombus.

Section 5.5 Continues…..

2. Definition A rectangle is a parallelogram with four

congruent angles.Rectangle conjectures: 1 The diagonals of a rectangle are congruent and

bisect each other.

Section 5.5 Continues…..

3. Definition A square is an equiangular rhombus or

equilateral rectangle. Conjecture:1. The diagonals of a square are congruent

perpendicular and bisect each other.

Section 5.7 Proving Quadrilateral Properties.

Day 84 1/9/2013 Objectives:Use flowchart proofing to

proof properties of different quadrilaterals.

Review conjectures of sections 5.1-5.7.

Assignment Class Work Go over some of the problems

in the hand out. Finish the hand out.

Lab Day

Day 84 1/10/2013Objectives:• Practice and review

concepts learned on chapter 2.

Assignment Class work • Finish the assigned sections

Day 85 1/11/2013 Note Book Quiz

• Write and sketch a figure to illustrate all conjectures of the following dates. Create a problem and use each conjecture to solve.

• Day 78 12/17/2012 Kite,… section 5.3• Day 79 12/19/2012 Section 5.4• Day 82 1/7/2013 Section 5.5• Day 83 1/8/2013 Section 5.6

Chapter 5 Review

Day 86 1/14/2013 Objectives: Review properties of

Quadrilaterals. Use the conjectures to solve

problems. Block schedule

Assignment

Class Work Note book quiz is due. Chapter 5 reviewHand out. Chapter 5 test.

Section 6.1-6.2 Circle

Day 88 1/16/2013 Objectives: Review basic properties of a

circle and circle vocabulary. Discover properties of a

tangent of a circle.Learn more vocabulary. Block schedule.

Assignment Class Work • Go over the warm up. • Complete the vocabulary of

section 6.1-6.2.• Write one example for each

conjecture. Class Work Finish the hand out.

Section 6.1 Vocabulary and Conjectures.

1.Tangent Conjecture• A tangent to a circle is perpendicular to the radius to

the point of tangency.

Section 6.1 …….

2. Tangent Segment Conjecture Tangent segments of a circle from a point outside of the

circle are congruent.

Section 6.1 Vocabulary

1.Tangent Circles are circles that are tangent to the same line.

2. Internally tangent circles 3. Externally tangent circles

Section 6.2 Vocabulary and Conjectures

• 1. Central angle

A central angle has its vertex at the center of the circle.

Section 6.2……

2.Inscribed AngleA inscribed angle has its vertex on the circle and its

sides are chords.

Section 6.2…..• 1. Chord Central Angle Conjecture If two chords in a circle are congruent, then they

determine two central angles that are congruent.

Section 6.2…

• 2. Chord Arc ConjectureIf two chords are congruent, then the intercepted arcs

are congruent.

Section 6.2……• 3. Perpendicular to a Chord ConjectureThe perpendicular from the center of the circle to a

chord is the bisector of the chord.

Section 6.2………..4. Chord Distance to Center Conjecture• Two congruent chords in a circle are equidistant from

the center of the circle.

Section 6.2….• 5. Perpendicular Bisector of a Chord Conjecture. The perpendicular bisector of a chord passes through

the center of the circle.

Lab

Day 99 1/17/2013Objectives:• Practice conjectures of

chapter 5. • Kite, Trapezoid,

Parallelogram, Rectangle ,Rhombus, and Square.

Assignment • Finish the assigned section.

Section 6.1-6.2 Circle

Day 100 1/22/2013 Objectives: Review basic properties of a

circle and circle vocabulary. Discover properties of a

tangent of a circle.Learn more vocabulary. Block schedule.

Assignment Class Work • Go over the warm up. • Complete the vocabulary of

section 6.1-6.2.• Write one example for each

conjecture. Class Work Finish the hand out.

Sections 6.3 Arcs and Angles


between the inscribed angle of a circle and its intercepted arc.

Block Schedule

Assignment Class Work • Go over the warm up • Go over questions from the

hand out. • Section 6.1-6.2 hand out

due. • New hand out due in the

end of the class.

Conjectures Section 6.3

1. Inscribed Angle Conjecture• The measure of an angle inscribed in a circle is half of the

measure of the inscribed Arc.

6.3 Continues …..2.Inscribed Angle Intercepting Arc Conjecture.

Inscribed angles that intercept the same arc are congruent.

6.3 Continues ……3. Angles Inscribed a Semicircle Conjecture Angles inscribed in a semicircle are right angles.

6.3 Continues ……4.Cyclic Quadrilateral Conjecture The opposite angles of a cyclic quadrilateral are

supplementary.

6.3 Continues ……5. Parallel Lines Intercepted Arc Conjecture • Parallel lines intercept congruent arcs on a

circle.

Lab Day Day 102 1/24/2013Objectives:• Interim Assessment Test • Practice sections 6.1-6.2 on

Carnegie Learning .

Assignment Class Work • Finish the Interim

Assessment Test • Work on Carnegie Learning• Finish the assigned sections.

Sections 6.3 Arcs and Angles


between the inscribed angle of a circle and its intercepted arc.

Block Schedule

Assignment Class Work • Hand out • “I was out sick”

Section 6.5

Day 104 1/29/2013

Objectives:• Calculate π, the ratio of the

circumference of a circle to its diameter.

Assignment Class WorkGo over the warm Go over the conjectures of section 6.5. Homework Page 337 # 1-10 all.

Section 6.7 Arc Length

Day 105 1/30/2013Objectives:Discover the Arc Length formula.Apply the Arc Length formula.

Assignment Class Work • Go over the warm ups.• Go over the examples and

arc length conjecture. Homework • Page 351 # 1-9 all.

Lab

Dai 106 1/31/2013 Objectives:• Practice conjectures of

sections 6.1-6.7

Assignment Class Work • Finish the assigned sections.• If the cognitive tutoring

does not work on problem 1-10 page 359.

Documents

Geometry in Nature and in Art Day 2 (8/21/2012) Objectives: Use geometry to create art designs. Identify reflectional and rotational symmetry. Assignment