1 5 Segment Angle Bisectors Geometry Mrs Blanco

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 an angle.

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

Ex 1 a: Find the midpoint of CD if C(-12, -9) & D(2, 10). Ex 1 b: You Try: Find the Midpoint of CD C(-1. 5, 4) & D(0. 25, -1).

Ex 2 a: 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 2 b: 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. k A M B

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

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

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

Ex 4 a: If RQ bisects PRS. Solve for x x+40 = 3 x-20 40 = 2 x-20 60 = 2 x 30 = x

Last Example: Ex 4 b: If BD bisects ABC. Solve for x 1/2 x+20 = 3 x-85 20 = 2 ½ x-85 105 = 2 ½ x 42 = x

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