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CONGRUENT ANGLES & BISECTOR OF AN ANGLE. Definition of Congruent Angles. “Two angles are said to be congruent if and only if they have the same measure.” There is a phrase “if & only if”which means that the definition is two way. 1) If the angles are congruent, then they are equal.
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Definition of Congruent Angles • “Two angles are said to be congruent if and only if they have the same measure.” There is a phrase “if & only if”which means that the definition is two way. • 1) If the angles are congruent, then they are equal. • 2) If the angles are equal, then they are congruent.
ILLUSTRATION: • A 55° 55° B • In the figure, • If A = 55 ° and B = 55 °, then • A B • If A B , then • mA =mB
Definition of Bisector of an Angle • “The bisector of an angle is a ray that divides an angle into two congruent angles.” ILLUSTRATION: In the figure, if ray BF A F Is an angle bisector, then It divides ABC into two B C equal parts. And ABF CBF. NOTE: LIKE MARKINGS INDICATES EQUAL PARTS
Angle Addition Postulate • “If F is in the interior of ABC, then m ABF +m FBC= m ABC.” Then ray BF is called angle bisector of the angle. A F B C NOTE: LIKE MARKINGS INDICATES EQUAL PARTS
