5.4(a) Notes: The Angle Addition Postulate and Supplementary Angles

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Presentation transcript:

5.4(a) Notes: The Angle Addition Postulate and Supplementary Angles Date: 5.4(a) Notes: The Angle Addition Postulate and Supplementary Angles Lesson Objective: Discover the angle addition postulate. Write proofs involving supplementary and complementary angles. CCSS: G.CO.9 Prove theorems about lines and angles. You will need: colored pens, PR This is Jeopardy!!!: This is the diagram and the answer for AB when AC = 125 and BC = 45.

Lesson 1: Angle Addition Postulate Draw / ABC with a measure of 125°. • •

Lesson 1: Angle Addition Postulate Draw / ABC with a measure of 125°. • B C A

Draw / DBC with a measure of 45°. What is the measure of / ABD? • B C A D

Angle Addition Postulate: D is in the interior of / ABC if and only if m/ ABD + m/ DBC = m/ ABC • • A D B C

Lesson 2: Use the Angle Addition Postulate If m/ 1 = 23° and m/ ABC = 131°, find m/ 3. Justify each step.

Lesson 3: Supplement Theorem Draw a line across the page about 4 blue lines down. Use your protractor to measure the line. _______

Lesson 3: Supplement Theorem Draw a line across the page below. Use your protractor to measure the line. 180° Draw / 1 with a measure of 50°. What is m/ 2? ______ What is m/ 1 + m/ 2? ______ 1 2 50°

Supplement Theorem: If 2 angles form a linear pair, then they are supplementary angles (they add up to 180°). Linear Pair: A pair of adjacent angles with noncommon sides that are opposite rays (they add up to 180°). Example: m/ 1 + m/ 2 = 180° 1 2

Lesson 4: Using the Supplement Theorem / 6 and / 7 form linear pair. If m/ 6 = 3x + 32 and m/ 7 = 5x + 12, find x, m/ 6, and m/ 7. Justify each step.