1. 1.5 Segment & Angle Bisectors Geometry Fall 2005 Mrs. Spitz

2. Standard/Objective Standard 3: Students will understand geometric concepts and applications. Objectives: Bisect a segment. Bisect an angle.

3. Assignment: pp. 38-40 #2-48 Even and Practice Quiz – pg. 42 #1-6 all

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

5. 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

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

7. Compass & Straightedge Tools used for creating geometric constructions We will do a project with these later.

8. 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

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

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

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

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

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