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Geometry Unit 1: Topic 1 SLT 1‐6

Foundations of Euclidean Geometry

NAME: ____________________________________

TEACHER:__________________________________

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Foundations of Euclidean Geometry – Capture Sheet

Name of Figure Example Diagram Definition

Point

Line

Plane

Line Segment

C

K

P

A B

C

Y

Z

X

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Ray

Angle

Acute Angle

Right Angle

Complimentary Angles

Obtuse Angle

V

W

U

T

V

R

Q

S

B

A

C

D

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Straight Angle

Supplementary Angles

Scalene Triangle

Isosceles Triangle

Equilateral Triangle

A

B

C

A

B C

D

E F

U T

V

W

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Right Triangle

Intersecting Lines

Perpendicular Lines

Parallel Lines

A

B

C

D

M

R

U T

S

H

J K

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SLT 1 Extending Foundations Investigating foundational geometric figures: Below are questions that require your investigation. Consider how you will explore each situation to answer the questions. Think about: What tools will you need? What figures will you draw? How will you arrange the geometric figures in your drawing? How many different configurations do you need to consider in making a valid conjecture? For each question below, justify your conjecture and be sure to describe your investigation techniques. 1) How many points are needed to define a unique line? 2) Describe the geometric figure formed by the intersection of two lines. 3) How many points are needed to define a unique plane? Are there any rules about the location of these

points? 4) Describe the geometric figure formed by the intersection of two planes. 5) How would you define the term “space”? 6) Is it possible to have two lines that do not intersect and are not parallel?

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F

H

J

K

G

L

Figure 2

Q

R

S Figure 4

A

B

C

Figure 3

A

CB

D

E

Figure 1

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What Do You See 2

C

D

E

F

G

H

J

K

A

B

D

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SLT 3 – Copying Line Segments and Angles

Use constructions to copy and label each of the segments below.

A B

C

D

F

E

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Use constructions to copy and label each of the angles below.

H

K

N

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Use constructions to copy and label the segments:

Use the segments above to construct the following:

1.) A line segment with the length of AB + EF.

2.) A line segment with the length of 2(AB).

A B

C

D

F

E

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Use constructions to copy and label the angles below:

Use the angles above to construct an angle with a measure of ∠H + ∠N

H

K

N

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SLT 3 – Applying Segment & Angle Constructions

Recreate the pattern on the board by copying the line segments and angle provided below. Copy them onto the next page.

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SLT 3 – Applying Segment & Angle Constructions

Copy them here to recreate the rhombus figure from the board.

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SLT 4 – Construct a Perpendicular Bisector

Family Reunion

The Johnson family is planning a family reunion. They would like to select a location that is exactly the same distance from their two hometowns. One family lives in Gaithersburg, MD, and the other family lives in Manhattan, NY. Help them determine a location so that they can begin making travel plans to meet.

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SLT 4 – Construct a Perpendicular Bisector

1. Use your compass and straight edge to make a construction on the map that will help you find a location for the family reunion. Describe how the construction will assist you in determining possible locations.

2. Grandpa suggests that the family meet in Philadelphia, PA. Use your construction to explain whether this is an appropriate meeting place.

3. Which city is halfway between Gaithersburg and Manhattan? How do you know?

4. Are there any other cities that are the same distance from each family’s hometown? How do you know?

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SLT 6 – Construct a Line Parallel to a Given Line Through a Point Not on the Line

Railway Map

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SLT 6 – Construct a Line Parallel to a Given Line Through a Point Not on the Line

Street Map

Construct the following using the criteria below and an appropriate tool: Main Street runs parallel to State Street, which passes through point A. State Street runs parallel to Capital Avenue, which passes through point B. Evergreen Road runs perpendicular to Main Street through point X. Eagle Avenue intersects Main Street and Evergreen Road, but is neither parallel nor perpendicular to

either. Ridge Road runs perpendicular to Main Street through point Y.

1) What is the relationship between Main Street and Capital Avenue? How do you know? 2) What is the relationship between Evergreen Road and Ridge Road? How do you know?

3) What is the relationship between Eagle Avenue and Ridge Road? How do you know?

Main Stree

t

X

Y

A

B

geometry unit 1: topic 1 - mathmrspierce.weebly.com file1. use your compass and straight edge to...

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