1.5 Segment & Angle Bisectors Geometry Mrs. Blanco.

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Presentation transcript:

1.5 Segment & Angle Bisectors Geometry Mrs. Blanco

Standard/Objective Standard 3: Students will understand geometric concepts and applications. Objectives: Find the Midpoint of a segment. Bisect a segment. Bisect an angle.

Midpoint The point on a segment that divides the segment into two congruent segments. (bisects a segment)

Ex 1a: Find the midpoint of CD if C(-12,-9) & D(2,10). Ex 1b: You Try: Find the Midpoint of CD C(-1.5,4) & D(0.25,-1).

Ex 2a: The midpoint of BD is M(-1,1). One endpoint is D(2,6). Find the coordinates of B. D M B(-4,-4) Ex 2b: You Try: Find the B if M(0,3) & D(-8,-1)

Segment Bisector A segment, ray, line, or plane that intersects a segment at its midpoint. A B M k

Angle Bisector A ray that divides an angle into two adjacent angles that are congruent. BD is an angle bisector of  ABC. B A C D

Ex 3a: If QS bisects  PQR & m  SQR=22 o, what is m  PQR and m  PQS ? m  PQS=22° m  PQR=44°

Ex 3b: If QS bisects  PQR & m  PQR=124 o, what is m  PQS and m  SQR ? m  PQS=62° m  SQR=62°

x+40 = 3x = 2x = 2x 30 = x Ex 4a: If RQ bisects  PRS. Solve for x

1/2x+20 = 3x = 2 ½ x = 2 ½ x 42 = x Last Example: Ex 4b: If BD bisects  ABC. Solve for x

Class practice— Pgs #18, 22, 26, 28, 32, 38, 39, 40, 41, 44, 46, 48, 52, 54,