2.1 Segment Bisectors. Definitions Midpoint – the point on the segment that divides it into two congruent segments ABM.

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Presentation transcript:

2.1 Segment Bisectors

Definitions Midpoint – the point on the segment that divides it into two congruent segments ABM

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 ABM D C

Find Segment Lengths M is the midpoint of AB. Find AM and MB. AM = MB = ½ (AB) = ½ (26) = 13 ABM 26

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

Use Algebra with Segment Lengths Line l is a segment bisector of AB. Find x. AM = MB 5x = 35 x = 7 ABM l 5x35

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 A M B y2y2 y 1 + y y1y1 x1x1 x 1 + x x2x2

The Midpoint Formula The coordinates of the midpoint of AB is: M x 1 + x 2, y 1 + y A M B y2y2 y 1 + y y1y1 x1x1 x 1 + x x2x2

Example 1 1 A (1, 2) B (7, 4) M Let (x 1, y 1 ) = (1, 2) Let (x 2, y 2 ) = (7, 4) M = 1 + 7, = (4, 3)

Guided Practice Pg. 56 # 1-10