Download 1.1 Building Blocks of Geometry

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:
Term
Read pages 28-32. Draw a picture and give a definition for the following terms.
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.
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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
1. Angle
Definition
Picture/Symbol
2. Vertex
3. Sides
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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.
Term
Definition
Picture/symbol
1. polygon
11
2. side
3. vertex
4. consecutive angles
5. consecutive vertices
6. consecutive sides
7. diagonal
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8. convex
9. concave
10. corresponding sides
11. perimeter
12. equilateral polygon
13. equiangular polygon
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14. regular polygon
Complete the EXERCISES on pages 56-58 # ________________.
*** Include a proper heading on your paper.
1.5 Triangles
LEQ: How are angles, polygons, triangles, quads, circles and solids measured?
Complete the VOCABULARY chart below.
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
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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
LEQ: How are angles, polygons, triangles, quads, circles and solids measured?
Complete the VOCABULARY chart below. Begin on page 64.
Term
Definition
Picture/Symbol
1. trapezoid
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2. kite
3. parallelogram
4. rhombus
5. rectangle
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6. square
Complete the EXCERCISES on pages 66-68 # _________________ on a separate piece of paper.
***Use a proper heading on your paper.
1.7 Circles
LEQ: How are angles, polygons, triangles, quads, circles and solids measured?
Complete the VOCABULARY chart below.
Term
Definition
Picture/symbol
1. circle
2. radius
3. center
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4. chord
5. diameter
6. tangent
7. point of tangency
8. congruent circles
9. concentric circles
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10. arc
11. endpoints
12. semicircle
13. minor arc
14. major arc
15. arc measure
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16. central angle
Complete EXCERSISES on pages 72-74 # _________________.
Use a separate piece of paper and include a proper heading.
1.8 Space Geometry
LEQ: How are angles, polygons, triangles, quads, circles and solids measured?
Complete the VOCABULARY chart below. Begin on page 75.
Term
Definition
Picture/Symbol
1. space
2. isometric drawing
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3. cylinder
4. cone
5. prism
6. pyramid
7. sphere
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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.
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.
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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
Volumes 1 and 2 of a two-volume set
of math books sit next to each other
on a shelf. They sit in their proper
order: Volume 1 on the left and
Volume 2 on the right. Each front and
back cover is _18
_-inch thick, and the
pages portion of each book is 1-inch
thick. If a bookworm starts at the first
page of Volume 1 and burrows all the
way through to the last page of
Volume 2, how far will it travel?
Take a moment and try to solve the
problem in your head.
Write your answer to Example A here:
Example B
Harold, Dina, and Linda are
standing on a flat, dry field
reading their treasure map.
Harold is standing at one of
the features marked on the
map, a gnarled tree stump,
and Dina is standing atop a
large black boulder. The map
shows that the treasure is
buried 60 meters from the
tree stump and 40 meters
from the large black boulder.
Harold and Dina are standing
80 meters apart. What is the
locus of points where the
treasure might be buried?
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Write your answer to Example B here:
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 congruent
angles, so they are equiangular
Squares are both equilateral and equiangular.
Write your answer to Example C here:
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Complete the VOCABULARY chart below.
Term
Definition
Picture/symbol
1. Venn diagram
Complete EXCERSISES pages 84-87 # __________________ on a separate piece of paper, using a proper
heading.
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