PS 1 Foundations of Geometry

Mrs. DeYoung, Sep 15, 2018

Table of Contents

  1. 1.2.1a Terminology
    1. Identify Terminology (1)
    2. Identify Terminology (2)
  2. 1.2.1b Segment/Angle Addition Postulates
    1. Exploring Segment Addition Postulate
    2. Use the Segment Addition Postulate
    3. Exploring Angle Addition Postulate
    4. Using Angle Addition Postulate
  3. 1.2.2 Congruent Compliments and Supplements
    1. Exploring Congruent Supplements
    2. Exploring Congruent Complements
  4. 1.2.3 Find Complimentary and Supplementary Angles
    1. Complementary Angles Practice
    2. Supplementary Angles Practice
  5. 1.3.1 Apply theorems to solve for angles and lengths
    1. Midpoint/Segment Addition Postulate
    2. Vertical Angles Theorem
    3. Angle Bisector/Angle Addition Postulate
  6. 1.3.2 Solve using Congruent Compliments and Supplements
    1. Solving Congruent Complements
  7. 1.3.3 Proofs
    1. Proof Tips!
    2. Two Column Proofs
  8. 1.3.4 Constructions
    1. Construct a Congruent Segment
    2. Constructing an Angle Bisector
    3. Construct a Congruent Angle

1.

1.2.1a Terminology

[url]https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-intro-euclid/v/language-and-notation-of-basic-geometry[/url]

  • 1. Identify Terminology (1)
  • 2. Identify Terminology (2)

1.1.

Identify Terminology (1)

On a piece of paper, name each of the following, using the figure below:[br][br]1. A plane[br]2. A point[br]3. A ray[br]4. A line[br]5. A line segment[br]6. Vertical angles[br][br][b]**Be sure to use proper notation![/b]
– Mrs. DeYoung

1.2.

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2.

1.2.1b Segment/Angle Addition Postulates

  • 1. Exploring Segment Addition Postulate
  • 2. Use the Segment Addition Postulate
  • 3. Exploring Angle Addition Postulate
  • 4. Using Angle Addition Postulate

2.1.

Exploring Segment Addition Postulate

Directions:
1. Move point B anywhere on screen, paying attention to the lengths of each segment.[br]2. Then move point C, paying attention to the lengths of each segment.[br]3. Answer the questions at the end of the applet.
Create an equation to describe the relationship of the segments
Do you think your equation would work for any segment? Why or Why not?
– Mrs. DeYoung

2.2.

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2.3.

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2.4.

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3.

1.2.2 Congruent Compliments and Supplements

  • 1. Exploring Congruent Supplements
  • 2. Exploring Congruent Complements

3.1.

Exploring Congruent Supplements

Use the figure below to answer the questions that follow
How would you describe ∠AEB and ∠BED?
What is m∠BED?
How would you describe ∠CED and ∠BED?
What is m∠CED?
How would you describe ∠CED and ∠AEB?
– Mrs. DeYoung

3.2.

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4.

1.2.3 Find Complimentary and Supplementary Angles

  • 1. Complementary Angles Practice
  • 2. Supplementary Angles Practice

4.1.

Complementary Angles Practice

Find the complements to the angles pictured below.
Find the complement of ∠B:
Find the complement of ∠E:
Find the complement of ∠H:
– Mrs. DeYoung

4.2.

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5.

1.3.1 Apply theorems to solve for angles and lengths

  • 1. Midpoint/Segment Addition Postulate
  • 2. Vertical Angles Theorem
  • 3. Angle Bisector/Angle Addition Postulate

5.1.

Midpoint/Segment Addition Postulate

Using the diagram, answer the question below.
Matt and Britney are on their way to Ann Arbor to see a University of Michigan football game. According to their GPS, the distance from Grand Rapids to Ann Arbor is 132 miles. They planned to stop for breakfast in Lansing, which is the midpoint of the trip, but they had to stop for gas. If Lansing is still 19 miles away from the gas station, how many miles have they traveled so far?
What theorems did you use to solve this problem?
– Mrs. DeYoung

5.2.

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5.3.

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6.

1.3.2 Solve using Congruent Compliments and Supplements

  • 1. Solving Congruent Complements

6.1.

Solving Congruent Complements

∠B is complementary to ∠D and ∠D is complementary to ∠F. If m∠B = (10x - 15)⁰ and m∠F. = (7x - 6)⁰, what is m∠B?
∠B is complementary to ∠D and ∠D is complementary to ∠F. If m∠B = (3x - 4)⁰ and m∠F. = (2x+4)⁰, what is m∠B?
– Mrs. DeYoung

7.

1.3.3 Proofs

  • 1. Proof Tips!
  • 2. Two Column Proofs

7.1.

Proof Tips!

1. Always start a proof with your given information[br]2. End with whatever you were trying to prove[br]3. Work out any math before you start[br]4. Label the left column "statements" and the right column "reasons"[br]5. LABEL YOUR PICTURE
– Mrs. DeYoung

7.2.

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8.

1.3.4 Constructions

  • 1. Construct a Congruent Segment
  • 2. Constructing an Angle Bisector
  • 3. Construct a Congruent Angle

8.1.

Construct a Congruent Segment

When finished, you should have something that looks like this:
– Mrs. DeYoung

8.2.

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8.3.

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