1.5 Segment & Angle Bisectors Geometry Fall 2005 Mrs. Spitz

Learning Targets I can bisect a segment. I can bisect an angle.

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 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 a project 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

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) 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. BD is an angle bisector of <ABC. A D B C

Ex: 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

Sage and Scribe pages 38-40 Work on #2-48 Even # ONLY

Learning Check Practice Quiz – pg. 42 #1-6 all

REFERENCE http://www.taosschools.org/ths/Departments/MathDept/quintana/GeometryPPTs/index.htm