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### GBK Geometry

Jordan Johnson

Today’s plan

- Greeting
- Review Asg #17
- Practice Quiz
- Lesson:
- Homework / Questions
- Clean-up

Practice Quiz (~5 min)

- For each of these statements, name the postulate or theorem that justifies the statement:
- If x + 1 = 2x, then 1 = x.
- If x⁄3 – 6 = 3, then x⁄3 = 9.
- If A + B = 70° and A + B + C = 180°,then 70° + C = 180°.
- If X-Y-Z, then XY + YZ = XZ.
- Let d be the distance between A and B.

Warm-up Solutions

- For each of these statements, name the postulate or theorem that justifies the statement:
- If x + 1 = 2x, then 1 = x. The subtraction property
- If x⁄3 – 6 = 3, then x⁄3 = 9. The addition property
- If A + B = 70° and A + B + C = 180°,then 70° + C = 180°. The substitution property
- If X-Y-Z, then XY + YZ = XZ.The Betweenness of Points Theorem
- Let d be the distance between A and B.The Ruler Postulate

Definitions

- Two angles are complementary iff their measures add up to 90°.
- Each of these angles is the other’s complement.

- Two angles are supplementary iff their measures add up to 180°.
- Each of these is the other’s supplement.

New Theorems

- Complements of the same angle are of equal size.
- Supplements of the same angle are of equal size.

Theorem 3 – Proof

Given: 1 and 2 are complements of 3.

Prove: 1 = 2

Statement

Reason

- 1 and 2 are complements of 3.
- 1 + 3 = 90°2 + 3 = 90°
- 1 + 3 = 2 + 3
- 1 = 2

- Given.
- Definition of complementary.
- Substitution.
- Subtraction (– 3)

Definitions

- Opposite rays point in opposite directions and share the same endpoint.
- In other words, they form a straight angle (180°).

- Two angles form a linear pair iff they share a common side and their other sides are opposite rays.
- Two angles are vertical angles iff the sides of one are opposite rays to the sides of the other.

Theorems

- Theorem 5 (“Linear Pair Theorem”):
- The angles in a linear pair are supplementary.

- Theorem 6 (“Vertical Angles Theorem”):
- Vertical angles are congruent.

Homework

- From Chapter, Section:

Clean-up / Reminders

- Pick up all trash / items.
- Push in chairs (at front and back tables).
- See you tomorrow!

Practice Quiz

- When you are finished, put away your pencil and take out two pens/pencils of different color for corrections.
- First color = careless mistakes / “I knew that!”
- Second color = things not understood / “I should review this!”

- Come to my desk to pick up a solutions sheet,and check your work.
- When you’re done with the solutions sheet, bring it back to me.

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