Angle Addition Postulate First, let’s recall some previous information from last week…. We discussed the Segment Addition Postulate, which stated that.

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Angle Addition Postulate

Presentation transcript:

Angle Addition Postulate First, 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… JKL

Angle Addition Postulate 50  65  A B C O If B lies on the interior of  AOC, then m  AOB + m  BOC = m  AOC. m  AOC = 115  Slide 2

Example 1: This is a 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 = ______ ABC D 134° 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 =  114  19  Plug in what you know. Solve. 46° Example 2:Slide 3

Algebra Connection Slide 4 R S T V Given: m  RSV = x + 5 m  VST = 3x - 9 m  RST = 68 Find x. m  RSV + m  VST = m  RST x x – 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 = = 23 m  VST = 3x - 9 m  VST = 3(18) – 9 = 45 Check: m  RSV + m  VST = m  RST = 68

Algebra Connection Slide 5 B Q 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 = 35 m  CQD = 83 m  BQD = 118 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 = 118