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Angle Addition Postulate Presentation
- 1. Angle Addition PostulateFirst, let’s recall some previous information from last week…. We discussed the Segment Addition Postulate , which stated that we could add the lengths of adjacent segments together to get the length of an entire segment. For example: JK + KL = JL If you know that JK = 7 and KL = 4, then you can conclude that JL = 11. The Angle Addition Postulate is very similar, yet applies to angles. It allows us to add the measures of adjacent angles together to find the measure of a bigger angle… J K L
- 2. Angle Addition PostulateA B C O If B lies on the interior of AOC, then m AOB + m BOC = m AOC. m AOC = 115 50 65
- 3. Examples: This isa special example, because the two adjacent angles together create a straight angle. Predict what m ABD + m DBC equals. ABC is a straight angle, therefore m ABC = 180. m ABD + m DBC = m ABC m ABD + m DBC = 180 So, if m ABD = 134, then m DBC = ______ 46 G H J K Given: m GHK = 95 m GHJ = 114 . Find: m KHJ . The Angle Addition Postulate tells us: m GHK + m KHJ = m GHJ 95 + m KHJ = 114 m KHJ = 19. 19 Plug in what you know. Solve. 46 ° A B C D 134° 95 114
- 4. Algebra Connection RS T V Given: m RSV = x + 5 m VST = 3x - 9 m RST = 68 Find x. m RSV + m VST = m RST x + 5 + 3x – 9 = 68 4x- 4 = 68 4x = 72 x = 18 Set up an equation using the Angle Addition Postulate. Plug in what you know. Solve. Extension : Now that you know x = 18, find m RSV and m VST. m RSV = x + 5 m RSV = 18 + 5 = 23 m VST = 3x - 9 m VST = 3(18) – 9 = 45 Check: m RSV + m VST = m RST 23 + 45 = 68
- 5. Algebra Connection BQ D C m BQC = x – 7 m CQD = 2x – 1 m BQD = 2x + 34 Find x, m BQC , m CQD , m BQD . m BQC + m CQD = m BQD 3x – 8 = 2x + 34 x – 7 + 2x – 1 = 2x + 34 x – 8 = 34 x = 42 m BQC = x – 7 m BQC = 42 – 7 = 35 m CQD = 2x – 1 m CQD = 2(42) – 1 = 83 m BQD = 2x + 34 m BQD = 2(42) + 34 = 118 Check: m BQC + m CQD = m BQD 35 + 83 = 118 x = 42 m BQC = 35 m CQD = 83 m BQD = 118