2.1 Segment Bisectors

1. 2.1 Segment Bisectors

2. Definitions • Midpoint – the point on the segment that divides it into two congruent segments A M B

3. Definitions • Segment bisector – a segment, line, ray, or plane that intersects a segment at its midpoint • Bisect – to divide the segment into two congruent segments C A M B D

4. Find Segment Lengths • M is the midpoint of AB. Find AM and MB. • AM = MB = ½ (AB) • = ½ (26) • = 13 26 A M B

5. Find Segment Lengths • P is the midpoint of RS. Find PS and RS. • RP = PS so PS = 7 • RS = 2 (RP) • = 2 (7) • = 14 R P S 7

6. Use Algebra with Segment Lengths • Line l is a segment bisector of AB. Find x. AM = MB 5x = 35 x = 7 5x 35 A M B l

7. The Midpoint Formula • The coordinates of the midpoint of a segment are the averages of the x-coordinates and the y-coordinates of the endpoints B y2 y1 + y2 ---------- 2 M A y1 x1 x1 + x2 --------- 2 x2

8. The Midpoint Formula • The coordinates of the midpoint of AB is: M x1 + x2 , y1 + y2 2 2 B y2 y1 + y2 ---------- 2 M A y1 x1 x1 + x2 --------- 2 x2

9. Example B (7, 4) M A (1, 2) 1 1 Let (x1, y1) = (1, 2) Let (x2, y2) = (7, 4) M = 1 + 7 , 2 + 4 2 2 = (4, 3)

10. Guided Practice • Pg. 56 # 1-10