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Do Now Take out all sub work and have it on your desk for me to come around and check.

Do Now Take out all sub work and have it on your desk for me to come around and check. Proving Angles Congruent. Objectives: 1. Identify angle pairs. 2. Prove theorems about angles. Vertical angles : angles whose sides form 2 pairs of opposite rays. ∠1 and ∠3 are vertical angles.

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Do Now Take out all sub work and have it on your desk for me to come around and check.

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  1. Do Now Take out all sub work and have it on your desk for me to come around and check.

  2. Proving Angles Congruent • Objectives: 1. Identify angle pairs. 2. Prove theorems about angles.

  3. Vertical angles: angles whose sides form 2 pairs of opposite rays ∠1 and ∠3 are vertical angles

  4. Investigation • Take out a piece of paper a draw the following figure: • Fold the sides of < 1 and < 2. • Fold the sides of < 3 and < 4. • Make a conjecture (a guess or a theory) about vertical angles.

  5. What did you discover? • Vertical angles are congruent!

  6. Why is this important? • We can use vertical angle congruence to find missing angle measures.

  7. What is the measure of angle b?

  8. Find x!!

  9. Other Types of Angle Pairs • Adjacent Angles: Two coplaner angles with a common side, a common vertex, and no common interior points.

  10. Complementary Angles: Two angles whose measures have a sum of 90 degrees. • Each angle is called the compliment of the other.

  11. Supplementary Angles: Two angles whose measures have a sum of 180 degrees. • Each angle is called the supplement of the other.

  12. Linear pair: Adjacent angles whose noncommon sides are opposite rays (on a line) The measures of angles in a linear pair add to 180˚ ∠1 and ∠2 are a linear pair • m∠1 + m ∠2 = 180 ˚

  13. Angles in a linear pair are supplementary!!

  14. Using everything wehave justlearned… how can we prove vertical angles are congruent? • We are given the information that < 1 and < 2 are vertical angles. • We want to prove that < 1 ≅< 2.

  15. Think, Pair, Share • I am going to present you with two questions. • You will have 2 minutes to think to yourself about the question. • You will then have 3 minutes to turn to a partner and discuss the question and your response to it. • Be prepared to share your answer with the class.

  16. Question 1 • If two angles are supplements of the same angle (or of congruent angles), are they congruent?

  17. Question 2 • If two angles are complements of the same angle (or of congruent angles), are they congruent?

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