CK-12 Geometry Concepts

http://www.ck12.org Chapter 1. Basics of Geometry

Example C

IsOPthe angle bisector of^6 SOT? Ifm^6 ROT= 165 ◦, what ism^6 SOPandm^6 POT?

Yes,OPis the angle bisector of^6 SOTaccording to the markings in the picture. Ifm^6 ROT= 165 ◦andm^6 ROS= 57 ◦,
thenm^6 SOT= 165 ◦− 57 ◦= 108 ◦. Them^6 SOPandm^6 POTare each half of 108◦or 54◦.

Watch this video for help with the Examples above.

MEDIA

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CK-12 Foundation: Chapter1CongruentAnglesandAngleBisectorsB

Vocabulary

When two geometric figures have the same shape and size then they arecongruent. Anangle bisectoris a ray that
divides an angle into two congruent angles, each having a measure exactly half of the original angle.

Guided Practice

For exercises 1 and 2, copy the figure below and label it with the following information:

1.^6 A∼=^6 C
2.^6 B∼=^6 D
3. Use algebra to determine the value of d:

Answers:

1. You should have corresponding markings on^6 Aand^6 C.


2. You should have corresponding markings on^6 Band^6 D(that look different from the markings you made in #1).


3. The square marking means it is a 90◦angle, so the two angles are congruent. Set up an equation and solve:

7 d− 1 = 2 d+ 14

5 d= 15

d= 3

Practice

For 1-4, use the following picture to answer the questions.

1. What is the angle bisector of^6 T PR?


2. What ism^6 QPR?


3. What ism^6 T PS?


4. What ism^6 QPV?

For 5-6, use algebra to determine the value of variable in each problem.