1 5 Segment Angle Bisectors Geometry Learning Targets

1. 5 Segment & Angle Bisectors Geometry

Learning Targets • Bisecting segments • Bisecting angles

Always Remember! • If they are congruent, then set their measures equal to each other!

Midpoint • The point that bisects a segment. • Bisects? splits into 2 congruent pieces A 12 x+3=10 x+5 2 x=2 x=1 M 10 x+5 B

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

Midpoint Formula • Used for finding the coordinates of the midpoint of a segment in a coordinate plane. • If the endpoints are (x 1, y 1) & (x 2, y 2), then

Ex: Find the midpoint of SP if S(-3, -5) & P(5, 11).

Ex: The midpoint of AB is M(2, 4). One endpoint is A(-1, 7). Find the coordinates of B.

Angle Bisector • A ray that divides an angle into 2 congruent adjacent angles. A D B C BD is an angle bisector of <ABC.

Ex: If FH bisects EFG & m EFG=120 o, what is m EFH? E H F G

Last example: Solve for x, and the angles. • The angle below is bisected into 2 * If they are congruent angles: congruent, set them equal to each other, then solve! o 40 + x x+40 = 3 x-20 o 3 x-20 40 = 2 x-20 60 = 2 x 30 = x

Last Example cont. • Substitute x = 30 into one of the equations. • Since the angles are congruent, we will know the measure of both • X + 40 = (30) + 40 = 70 o

Classwork/Homework • pages 38 and 39 – Problems 1 -29 odds