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September 05, 2014 Section 1.5: Exploring Angle Pairs Objective: To identify special angle pairs and use their relationships to find angle measures a pair of adjacent angles whose noncommon sides are opposite rays (form a straight angle) a ray that divides an angle into two congruent angles (endpoint is at the vertex) 2 angles with a common side, a common vertex, and no common interior points two angles whose two angles whose two angles whose sides are opposite measures have a measures have a sum of 90 sum of 180 rays m_1 + m_2 = 180 1 2 September 05, 2014 Date: Section 1.5: Exploring Angle Pairs Objective: To identify special angle pairs and use their relationships to find angle measures Example 1: Identifying Angle Pairs Decide if each statement is true. Explain. a. _ _PAL and _ _LAM are adjacent angles. b. _ _PAO and _ _NAM are vertical angles. L P A 74o O c. _ _PAO and _ _NAO are supplementary. M 106o N September 05, 2014 Section 1.5: Exploring Angle Pairs Objective: To identify special angle pairs and use their relationships to find angle measures Example 2: Find Missing Angle Measurements What can you conclude from the information in the diagram? Congruent Angles: Linear Pairs: 5 4 Vertical Angles: 3 Adjacent Angles: Quick Check: Can you make each conclusion? Explain. a. TW WV c. _TWQ is a right angle. b. PW WQ d. TV bisects PQ 1 2 September 05, 2014 Section 1.5: Exploring Angle Pairs Objective: To identify special angle pairs and use their relationships to find angle measures Example 3: Finding Missing Angle Measures _ _ _ABC and _ _DBC are a linear pair. m_ABC = 3x+19, and m_DBC = 7x-9. _ What are the measures of _ _ABC and _ _DBC? _ADB and _ _BDC are a linear pair. m_ADB = 3x+14 and _ Quick Check: _ _ _ m_BDC = 5x-2. What are m_ADB and m_BDC? _ September 05, 2014 Section 1.5: Exploring Angle Pairs Objective: To identify special angle pairs and use their relationships to find angle measures Example 4: Using and Angle Bisector to Find Angle Measures _ _ LM bisects _ _JLN. If m_JLM = 42o, what is m_JLN? _ Quick Check: KM bisects _ _JKL. If m_JKL = 72o, what is m_JKM? _ September 05, 2014 Homework: P. 38 #7-28 *Bring a compass to class on Monday*