Chapter 2 Segments and Angles

Section 2 Angle Bisectors

An ________________________________ is a ray that divides an angle into two angles that are congruent. In the photograph of the hang glider, BD bisects <ABC because it divides the angle into two congruent angles. If BD bisects <ABC, then the measures of <ABD and <DBC are half the measure of <ABC. Also, the measure of <ABC is twice the measure of <ABD or <DBC

Example 1: Find Angle Measures BD bisects <ABC, and m<ABC = 110° Example 1: Find Angle Measures BD bisects <ABC, and m<ABC = 110°. Find m<ABD and m<DBC.

Checkpoint: Find Angle Measures HK Bisects <GHJ Checkpoint: Find Angle Measures HK Bisects <GHJ. Find m<GHK and m<KHJ.

Example 2: Find Angle Measures and Classify an Angle MP bisects <LMN, and m<LMP = 46°. a. Find m<PMN and m<LMN. b. Determine whether <LMN is acute, right, obtuse, or straight. Explain.

Checkpoint: Find Angle Measures and Classify an Angle QS bisects <PQR. Find m<SQP and m<PQR. Then determine whether <PQR is acute, right, obtuse or straight.

Example 3: Use Angle Bisectors In the kite, <DAB is bisected by AC, and <BCD is bisected by CA. Find m<DAB and m<BCD.

Checkpoint: Use Angle Bisectors 7. KM bisects <JKL. Find m<JKM 8 Checkpoint: Use Angle Bisectors 7. KM bisects <JKL. Find m<JKM 8. UV bisects <WUT. Find m<WUV and m<MKL. And m<WUT.

Example 4: Use Algebra with Angle Measures RQ bisects <PRS Example 4: Use Algebra with Angle Measures RQ bisects <PRS. Find the value of x.

Checkpoint: Use Algebra with Angle Measures BD bisects <ABC Checkpoint: Use Algebra with Angle Measures BD bisects <ABC. Find the value of x.