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SECTION 1.5 – EXPLORING ANGLE PAIRS Students will be able to: • identify special angle pairs and use their relationships to find angle measures Key Vocabulary adjacent angles complementary angles linear pair vertical angles supplementary angles angle bisector SECTION 1.5 – EXPLORING ANGLE PAIRS Definition Adjacent Angles: 2 coplanar angles with a common side, a common vertex, and no common interior points Vertical angles: 2 angles whose sides are opposite rays. Example Graphic Section 1.5 – Exploring Angle Pairs Definition Example Complementary angles: 2 angles whose measures have a sum of 90. Each angle is called the complement of each other < 3 < 4 Supplementary angles: 2 angles whose measures have a sum of 180. Each angle is called the supplement of the other And < < Graphic SECTION 1.5 – EXPLORING ANGLE PAIRS Problem 1: Use the diagram at the right. Is the statement true? Explain a. <AFE and <CFD are vertical angles. b. <BFC and <DFE are supplementary. c. <BFD and <AFB are adjacent angles. Concept Check • From an unmarked diagram, we can conclude if angles are • You cannot conclude from an unmarked diagram SECTION 1.5 – EXPLORING ANGLE PAIRS Problem 2: What can you conclude from the information in the diagram? SECTION 1.5 – EXPLORING ANGLE PAIRS Problem 2b: Can you make each conclusion from the information in the diagram? Explain. a. is congruent to b. <TWQ is a right angle c. is congruent to d. bisects SECTION 1.5 – EXPLORING ANGLE PAIRS A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. The angles of a linear pair form a _________________. SECTION 1.5 – EXPLORING ANGLE PAIRS Problem 3: <DEC and <FEC are a linear pair. What are the measures of < < ? SECTION 1.5 – EXPLORING ANGLE PAIRS An angle bisector is a ray that divides an angle into two congruent angles. Its endpoint is a the _________________. SECTION 1.5 – EXPLORING ANGLE PAIRS Problem 4: bisects < . If m< = 72, what is m< ? SECTION 1.5 – EXPLORING ANGLE PAIRS Lesson Check SECTION 1.5 – EXPLORING ANGLE PAIRS Lesson Check