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Measuring Angles Geometry vs Algebra Segments are Congruent – Symbol [ ] – AB CD – 1 2 Lengths of segments are equal. – Symbol [ = ] – AB = CD – m1 = m2 Angles Formed by 2 rays with the same endpoint – Vertex of the Angle B Symbol: [ ] Name it by: – Its Vertex A A – A number 1 – Or by 3 Points BAC - Vertex has to be in the middle 1 C How many s can you find? Name them. B A 1 2 3 s D – ADB or BDA – BDC or CDB – ADC or CDA Notice D (the vertex) is always in the middle. Can’t use D But 1 or 2 could be added. C Classifying Angles by their Measures Acute x° x < 90° Straight Right Obtuse x° x° x = 90° x > 90° x° x = 180° Postulate 1-7 Protractor Postulate Let OA & OB be opposite rays in a plane, & all the rays with endpoint O that can be drawn on one side of AB can be paired with the real number from 0 to 180. C A D O B Postulate 1-8 Angle Addition Postulate If point B is in the interior of MAD, then mMAB + mBAD = mMAD B M D A If MAD is a straight , then mMAB + mBAD = mMAD = 180° B D M A Finding measures (m ) Find mTSW if – mRSW = 130° – mRST = 100° W T R mRST + mTSW = mRSW 100 + mTSW = 130 mTSW = 30° S Addition mXYZ = 150 x 1 = 3x - 15 2 = 2x - 10 m1 + m2 = mXYZ (3x - 15) + (2x – 10) = 150 5x – 25 = 150 5x = 175 x = 35 Y Z Adjacent Angles Adjacent angles – two coplanar angles with a common side, a common vertex, and no common interior points. 1and 2 3and 4 Vertical Angles Vertical angles – two angles whose sides are opposite rays. 1and 2 3and 4 Complementary Angles Complementary angles – two angles whose measures have a sum of 90°. – Each angle is called the complement of the other. 1and 2 Aand B Supplementary Angles Supplementary angles – two angles whose measures have a sum of 180°. – Each angle is called the supplement of the other. 3and 4 Band C Identifying Angle Pairs Is the statement true or false? a. BFDand CFD are adjacent angles. b. AFBand EFD are vertical angles. c. AFEand BFC are complementary. F F T Perpendicular Lines Perpendicular lines – intersecting lines that form right angles Linear Pairs A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays. – The angles of a linear pair form a straight angle. Finding Missing Angle Measures KPLand JPL are a linear pair. mKPL 2 x 24, andmJPL 4 x 36. What are the measures of KPLand JPL ? Finding Missing Angle Measures mKPL mJPL 180 (2 x 24) (4 x 36) 180 6 x 60 180 6 x 120 x 20 mKPL 2x 24 2(20) 24 40 24 64 mJPL 4 x 36 4(20) 36 80 36 116 Angle Bisector An angle bisector is a ray that divides an angle into two congruent angles. – Its endpoint is at the angle vertex. – Within the ray, a segment with the same endpoint is also an angle bisector. The ray or segment bisects the angle. Using an Angle Bisector to Find Angle Measures AC bisectsDAB . If mDAB 58 , what is mDAC ? mCAB mDAC 58 mDAB mCAB mDAC 58 58 116