1.5 Segment and Angle Bisectors

1.5 Segment and Angle Bisectors

Goal • 1. To be able to use bisectors to find angle measures and segment lengths

Definitions • The Midpoint of a segment is the point that divides or bisects the segments into two congruent segments. • A Segment Bisector is a segment, ray, line, or plane that intersects a segment at its midpoint. • If segment AM is congruent to segment MB, then M is the midpoint of segment AB. • If M is the midpoint of segment AB, then segment AM is congruent to segment MB. • Bisects- Divides into congruent parts.

Examples

Ruler Postulate (Again) • Using a number line, we can find the midpoint of a line segment. But how? • Start by drawing a number line with points C=-4 and D=6. (Just an Example) • What is the distance between points C and D? • Where is the midpoint? Why? • The midpoint is the distance between two points divided by 2. • So the midpoint of the segment CD is 1.

The Midpoint Formula • If we know the coordinates of the endpoints of the segments, we can find the midpoint by using the midpoint formula. • If A(x₁, y₁) and E(x₂, y₂) are points in a coordinate plane, then the midpoint of ĀĒ has coordinates

Go to power point example 3 for examples

Example • The midpoint of segment RP is M(2,4). One endpoint is R(-1,7). Find the coordinates of the other endpoint. • (-1 + x)/2 = 2 (7 + y)/2=4 • -1 + x = 4 7 + y = 8 • X = 5 y = 1 • So the other endpoinot is P(5,1)

Class Work • Use the midpoint formula to find the midpoint of these coordinates • A (-1,7) and B (3,-3) • A (0,0) and B (-8,6)

Angle Bisector • An Angle Bisector is a ray that divides an angle into two adjacent angles that are congruent.

Example • Measure of angle ABD is (x + 40)° • Measure of angle DBC is (3x – 20)° • Solve for x • (x + 40)° = (3x - 20)° • X + 60 = 3x • 60 = 2x • X = 30

1.5 Segment and Angle Bisectors