Web viewLook around your classroom and identify examples of each of these terms: point, line, plane, line segment, congruent segments, midpoint of a segment, and ray

1.1 Building Blocks of Geometry Name______________________________MB#______

DISCOVERING GEOMETRY

LEQ: What are the characteristics of the basic building blocks of geometry?

Part I. VOCABULARY: Read pages 28-32. Draw a picture and give a definition for the following terms.

Term Definition Picture

1. Point

2. Line

3. Plane

4. Definition

5. Collinear

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6. Coplanar

7. Line Segment

8. Endpoints

9. Midpoint

10. Bisects

11. Ray

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12. Complete the Investigation on page 32:

In this lesson, you encountered many new geometry terms. In this investigation you will work as a group to identify models from the real world that represent these terms and to identify how they are represented in diagrams.

Step 1 Look around your classroom and identify examples of each of these terms: point, line, plane, line segment, congruent segments, midpoint of a segment, and ray.

Step 2 Identify examples of these terms in the photograph on page 32 in your textbook.

Step 3 Identify examples of these terms in the figure below.

Step 4 Explain in your own words what each of these terms means.

13. Complete the Exercises on page 33-35 # ________________ on a separate piece of paper.

****Be sure to include a proper heading with the Lesson #, page # and problem #.

Part 2.

14. Read page 36 and state the coordinate midpoint property below. Write the formula.

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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15. Give an example of how you would use midpoint.

__________________________________________________________________________________________________________________________________________________________________________

16. Complete Exercises on page 37 # _______________ on a separate piece of paper. (Remember to include a proper heading – see #13 above.)

1.2 Poolroom Math

LEQ’s: How do we classify angles, polygons, triangles, quads, circles and solids?

What is the difference between an incoming and outgoing angle?

Read pages 38-42 and complete VOCABULARY below:

Term Definition Picture/Symbol1. Angle

2. Vertex

3. Sides

4

4. Measure of an angle

5. Degrees

6. Reflex measure of an angle

7. Congruent

8. Angle Bisector

9. Incoming angle

10. Outgoing angle

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Complete the INVESTIGATION on page 41:

You will need: the worksheet Poolroom Math, a protractor

Pocket billiards, or pool, is a game of angles. When a ball bounces off the pool table’s cushion, its path forms two angles with the edge of the cushion. The incoming angle is formed by the cushion and the path of the ball approaching the cushion.

The outgoing angle is formed by the cushion and the path of the ball leaving the cushion. As it turns out, the measure of the outgoing angle equals the measure of the incoming angle.

Use your protractor to study these shots on the diagram below.

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Step 1 Use your protractor to find the measure of angle1. Which is the correct outgoing angle? Which point—A or B —will the ball hit?

Step 2 Which point on the cushion—W, X, or Y—should the white ball hit so that the ray of the outgoing angle passes through the center of the 8-ball?

Step 3 Compare your results with your group members’ results. Does everyone agree?

Step 4 How would you hit the white ball against the cushion so that the ball passes over the same spot on the way back?

Step 5 How would you hit the ball so that it bounces off three different points on the cushions without ever touching cushion line CP?

Complete the EXERCISES on page 42-46 # _________________.

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***Be sure to include a proper heading to include Lesson #, page # and problem #’s.

1.3 What’s a Widget?

LEQ: How are widgets used to help understand the classification of objects?

Complete the VOCABULARY chart below.

Term Definition Picture/symbol

1. counterexample

2. Steps to Creating a good definition. (3 steps).

3. Skew

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4. right angle

5. acute angle

6. obtuse angle

7. complementary angles

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8. supplementary angles

9. vertical angles

10. linear pair of angles

Complete EXERCISES pages 51-53 # ___________________ on a separate piece of paper.

***Be sure to include Lesson #, page # and problem #’s.

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1.4 Polygons

LEQ: How are angles, polygons, triangles, quads, circles and solids measured?

Begin on page 54.

# of Sides Name of Polygon

3

4

5

6

7

8

9

10

11

12

n

Complete the VOCABULARY chart below. Begin on page 54.


1. polygon

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2. side

3. vertex

4. consecutive angles

5. consecutive vertices

6. consecutive sides

7. diagonal

12

8. convex

9. concave

10. corresponding sides

11. perimeter

12. equilateral polygon

13. equiangular polygon

13

14. regular polygon

Complete the EXERCISES on pages 56-58 # ________________.

*** Include a proper heading on your paper.

1.5 Triangles



Term Definition Picture/Symbol

1. Assume

2. right triangle

3. acute triangle

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4. obtuse triangle

5. scalene triangle

6. equilateral triangle

7. isosceles triangle

8. Vertex angle

9. Base of isosceles triangle

15

10. Base angles of isosceles triangle

Complete EXERCISES on pages 62-63 # _________________ on a separate piece of paper.

***Use a proper heading on your paper.

1.6 Special Quadrilaterals




1. trapezoid

2. kite

16

3. parallelogram

4. rhombus

5. rectangle

6. square

Complete the EXCERCISES on pages 66-68 # _________________ on a separate piece of paper.

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***Use a proper heading on your paper.

1.7 Circles




1. circle

2. radius

3. center

4. chord

5. diameter

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6. tangent

7. point of tangency

8. congruent circles

9. concentric circles

10. arc

11. endpoints

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12. semicircle

13. minor arc

14. major arc

15. arc measure

16. central angle

Complete EXCERSISES on pages 72-74 # _________________.

Use a separate piece of paper and include a proper heading.

1.8 Space Geometry



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1. space

2. isometric drawing

3. cylinder

4. cone

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5. prism

6. pyramid

7. sphere

8. hemisphere

INVESTIGATION 1.8 Space Geometry.

Use the space below each statement for your sketches and answers.

Step 1 Make a sketch or use physical objects to demonstrate each statement in the list below.

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Step 2 Work with your group to determine whether each statement is true or false. If the statement is false, draw a picture and explain why it is false.

1. For any two points, there is exactly one line that can be drawn through them.

2. For any line and a point not on the line, there is exactly one plane that can contain them.

3. For any two lines, there is exactly one plane that contains them.

4. If two coplanar lines are both perpendicular to a third line in the same plane, then the two lines are parallel.

5. If two planes do not intersect, then they are parallel.

6. If two lines do not intersect, then they are parallel.

7. If a line is perpendicular to two lines in a plane, and the line is not contained in the plane, then the line is perpendicular to the plane.

Complete the EXERCISES on pages 78-80 # ________________ on a separate piece of paper.

1.9 A Picture is Worth a Thousand Words

LEQ: How are word problems solved by translating written information into a labeled diagram?

Read and answer examples A, B and C below.

By drawing diagrams, you apply visual thinking to problem solving. Let’s look at some examples that show how to use visual thinking to solve word problems.

Example A

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Volumes 1 and 2 of a two-volume setof math books sit next to each otheron a shelf. They sit in their properorder: Volume 1 on the left andVolume 2 on the right. Each front andback cover is _18_-inch thick, and thepages portion of each book is 1-inchthick. If a bookworm starts at the firstpage of Volume 1 and burrows all theway through to the last page ofVolume 2, how far will it travel?Take a moment and try to solve theproblem in your head.

Write your answer to Example A here:

Example B

Harold, Dina, and Linda arestanding on a flat, dry fieldreading their treasure map.Harold is standing at one ofthe features marked on themap, a gnarled tree stump,and Dina is standing atop alarge black boulder. The mapshows that the treasure isburied 60 meters from thetree stump and 40 metersfrom the large black boulder.Harold and Dina are standing80 meters apart. What is thelocus of points where thetreasure might be buried?Write your answer to Example B here:

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Example C

Create a Venn diagram to show the relationships among parallelograms, rhombuses, rectangles, and squares. Start by deciding, what is the most general group. What do parallelograms, rhombuses, rectangles, and squares have in common?

Now consider the special characteristics of rhombuses, rectangles, and squares.

Rhombuses have four congruent sides, so they are equilateral.

Rectangles have four congruentangles, so they are equiangular

Squares are both equilateral and equiangular.

Write your answer to Example C here:



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1. Venn diagram

Complete EXCERSISES pages 84-87 # __________________ on a separate piece of paper, using a proper heading.

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Documents

Web viewLook around your classroom and identify examples of each of these terms: point, line, plane, line segment, congruent segments, midpoint of a segment, and ray