1.5 Segment & Angle Bisectors

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Presentation transcript:

1.5 Segment & Angle Bisectors

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

Goal 1: Bisecting a Segment Midpoint: The point that bisects a segment. Bisects? splits into 2 equal pieces A M B 12x+3 10x+5 12x+3=10x+5 2x=2 x=1

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

Compass & Straightedge Tools used for creating geometric constructions We will do an activity with these later.

Midpoint Formula Used for finding the coordinates of the midpoint of a segment in a coordinate plane. If the endpoints are (x1,y1) & (x2,y2), then

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

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

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

Example: If FH bisects EFG & mEFG=120o, what is mEFH?

Last Example: Solve for x. * If they are congruent, set them equal to each other, then solve! x+40o x+40 = 3x-20 40 = 2x-20 60 = 2x 30 = x 3x-20o

Activity Time Use your compass, protractor and straightedge to work on the three activities in this section. Pg 33, 34, 36