LESSONS 1-5 TO 1-7Accelerated Algebra/Geometry

Mrs. Crespo 2012-2013

Lesson 1-5: Measuring Segments

RecapPostulate 1-5: Ruler Postulate

Postulate 1-6: Segment Addition Postulate (AB+BC=AC)

Definition of Coordinate, Congruent Segments and Midpoint.

A B C

A B C

20-2

Lesson 1-5: Examples

Example 1Comparing Segment Lengths

Example 2Using Addition Segment PostulateIf AB=25, find x. Then, find AN and NB.

A N B2x-6 x+7

AN + NB = AB(2x-6) +( x+7) = 253x + 1 = 253x = 24x = 24/3x = 8

AN = 2x – 6 = 2(8) – 6 = 16 – 6 = 10

NB = x + 7 = 8 +7 = 15

R M T5x+9 8x-36M

Lesson 1-5: Examples

RM = MT5x + 9 = 8x – 365x – 8x = -36 – 9-3x = -45x = -45/-3x = 15

RM = 5x + 9 = 5(15) + 9 = 75 + 9 = 84

MT = 8x – 36 = 8(15) – 36 = 120 – 36 = 84

RT = RM + MT = 84 + 84 = 168

Example 3Using MidpointM is the midpoint of segment RT. Find RM, MT, and RT.

Vocabulary and Key ConceptsPostulate 1-7: Protractor Postulate

Postulate 1-8: Angle Addition Postulate (m<AOB + m<BOC = m<AOC)

Definition of Angle Formed by two rays with the same endpoint.

T Q

B

Lesson 1-6: Measuring Angles

A B

CO

1

Vocabulary and Key ConceptsAcute Angle: measures between 00 and 900

Right Angle: measures exactly 900

Obtuse Angle: measures between 900 and 1800

Straight Angle: measures exactly 1800

Congruent angles: two angles with the same measure

x0

Lesson 1-6: Measuring Angles

x0

ACUTE ANGLE RIGHT ANGLE

0 < x < 900 x = 900

x0

900 < x < 1800

OBTUSE ANGLE

x0

x = 1800

STRAIGHT ANGLE

Example 1Naming Angles

Lesson 1-6: Examples

Name can be the number between the sides of the angle.

<3

AG

3

C

<CGA

<G

<AGC

Name can be the vertex of the angle.

Name can be a point on one side, the vertex, and a point on the other side of the angle.

or

Example 2Measuring and Classifying Angles

Lesson 1-6: Examples

Find the measure of each <AOC.

m<AOC =

Classify as acute, obtuse, or straight.

A

C

O

B

O

C

BA

600

ACUTE OBTUSE

m<AOC = 1500

Example 3Using the Angle Addition Postulate

Lesson 1-6: Examples

Suppose that m<1=42 and m<ABC=88. Find m<2

m<1 + m<2 = m<ABC 42 + m<2 = 88 m<2 = 88-42 m<2 = 460

B

A

C

1

2

Example 4Identifying Angle Pairs

Lesson 1-6: Examples

In the diagram, identify pairs of numbered angles as:

Complementary angles form 900 angles.

<3 and <4

5

1 2

34

Supplementary angles form 1800 angles.

Vertical angles form an “X”.

<1 and <2 <2 and <3

<1 and <3

Example 5Making Conclusions From A Diagram

Lesson 1-6: Examples

Can you make each conclusion from a diagram?

3

m<BCA + m<DCA = 1800

<B and <ACD are supplementary.

B

A

DC

<A <C≅

segment AB segment BC≅

VocabularyConstruction is using a straightedge and a compass to draw a geometric figure.

A straightedge is a ruler with no markings on it.

A compass is a geometric tool used to draw circles and parts of circles called arcs.

Lesson 1-7: Basic Construction

B

A

D

C

VocabularyPerpendicular lines are two lines that intersect to form right angles.

Lesson 1-7: Measuring Angles

A perpendicular bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint, thereby, bisecting the segment into two congruent segments.

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

L

KJ

T

Example 1Constructing Congruent Segments

Lesson 1-7: Examples

Construct segment TW congruent to segment KM.

STEP 1: Draw a ray with endpoint T.

K M

STEP 2: Open the compass the length of segment KM. W

STEP 3: With the same compass setting, put the compass point on point T. Draw an arc that intersects the ray. Label the point of intersection W.

Example 2Constructing Congruent Angles

Lesson 1-7: Examples

Construct <Y so that <Y is congruent to <G.

Y

750

G

E

F Z

750

<Y <G≅

1. Draw a ray with endpoint Y.2. With the compass point on G,

draw an arc that intersects both sides of <G. Label the points of intersection E and F.

3. With the same compass setting, put the compass point on point Y. Draw an arc that intersects the ray. Label the point of intersection Z.

4. Open the compass to the length EF. Keeping the same compass setting, put the compass on point Z. Draw an arc that intersects with the arc previously. Label the point of intersection X.

5. Draw ray YX to complete <Y.

X

Example 3Constructing The Perpendicular Bisector

Lesson 1-7: Examples

Given segment AB. Construct line XY so that line XY is perpendicular to segment AB at the midpoint M of segment AB. 1. Put the compass point on point

A and draw a long arc. Be sure the opening is greater than half of AB.

2. With the same compass setting, put the compass point on point B and draw another long arc. Label the points where the two arcs intersect as an X and Y.

3. Draw line XY. The point of intersection of segment AB and line XY is M, the midpoint of segment AB.

A B

X

Y

M

Example 4Finding Angle Measures

Lesson 1-7: Examples

Line WR bisects <AWB so that m<AWR=x and m<BWR=4x-48. Find m<AWB.

m<AWR = m<BWR x = 4x – 48 -3x = -48 x = 16

R

W

A

B

4x – 48

x

m<AWR = x = 16 m<BWR = 4x – 48 = 4(16) – 48 = 64 – 48 = 16

So, m<AWB = m<AWR + m<BWR = 16 + 16 = 32

HW: Posted on EdlineAccelerated Algebra/Geometry

Mrs. Crespo 2012-2013

Reference Textbook: Prentice Hall MathematicsGEOMETRY by Bass, Charles, Hall, Johnson, Kennedy

PowerPoint Created by Mrs. CrespoAccelerated Algebra/Geometry

Mrs. Crespo 2012-2013