Transcript Chapter 3
Angles CHAPTER 3 Angles SECTION 3-1 Angle – two rays with a common endpoint Vertex – common endpoint Sides – rays that make up the angle INTERIOR AND EXTERIOR Interior – all points between the two rays of the angle Exterior – all points outside of the two rays of the angle Points on the angle are not in the interior or the exterior The Angle Addition Postulate SECTION 3-3 POSTULATE 3-3 ANGLE ADDITION POSTULATE For any angle PQR, if A is in the interior of PQR, then PQA + AQR = PQR. ANGLE BISECTOR The ray with endpoint at the vertex of the angle, extending into the interior of the angle, that separates the angle into two angles of equal measure. Adjacent Angles and Linear Pairs of Angles SECTION 3-4 ADJACENT ANGLES Angles that share a common side and have the same vertex, but have no interior points in common. LINEAR PAIR Two angles form a linear pair if and only if they are adjacent and their noncommon sides are opposite rays. Complementary and Supplementary Angles SECTION 3-5 COMPLEMENTARY ANGLES Two angles are complementary if and only if the sum of their measures is 90. If two angles are complementary, each is the complement of the other SUPPLEMENTARY ANGLES Two angles are supplementary if and only if the sum of their measures is 180. If two angles are supplementary, each is the supplement of the other. EXAMPLES Find the complement and the supplement of each angle given. 74° 42 ° EXAMPLES Angles A and B are complementary. If A=x and B=5x, find x. Then find A and B. POSTULATE 3-4 If two angles form a linear pair, then they are supplementary. Congruent Angles SECTION 3-6 CONGRUENT ANGLES Two angles are congruent if and only if they have the same degree measure. VERTICAL ANGLES Two angles are vertical if and only if they are two nonadjacent angles formed by a pair of intersecting lines. THEOREM 3-1 Vertical angles are congruent. THEOREMS 3-2 AND 3-3 If two angles are congruent, then their complements are congruent. If two angles are congruent, then their supplements are congruent. THEOREMS 3-4 AND 3-5 If two angles are complementary to the same angle, then they are congruent. If two angles are supplementary to the same angle, then they are congruent. THEOREM 3-6 If two angles are congruent and supplementary, then each is a right angle. THEOREM 3-7 All right angles are congruent. Perpendicular Lines SECTION 3-7 PERPENDICULAR LINES Lines angle that intersect to form a right THEOREM 3-8 If two lines are perpendicular, then they form four right angles.