http://www.ck12.org Chapter 5. Relationships with Triangles
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter5AngleBisectorsB
Concept Problem Revisited
The airport needs to be equidistant to the three highways between the three cities. Therefore, the roads are all
perpendicular to each side and congruent. The airport should be located at the incenter of the triangle.
Vocabulary
Anangle bisectorcuts an angle exactly in half.Equidistantmeans the same distance from. A point is equidistant
from two lines if it is the same distance from both lines. When we construct angle bisectors for the angles of a
triangle, they meet in one point. This point is called theincenterof the triangle.
Guided Practice
- Is there enough information to determine if
−→
ABis the angle bisector of^6 CAD? Why or why not?−→
MOis the angle bisector of^6 LMN. Find the measure ofx.- A 100◦angle is bisected. What are the measures of the resulting angles?
Answers:
- No becauseBis not necessarily equidistant fromACandAD. We do not know if the angles in the diagram are
right angles.
2.LO=ONby the Angle Bisector Theorem.
4 x− 5 = 23
4 x= 28
x= 7- We know that to bisect means to cut in half, so each of the resulting angles will be half of 100. The measure of
each resulting angle is 50◦.
Practice
For questions 1-6,
−→
ABis the angle bisector of^6 CAD. Solve for the missing variable.1.
2.
3.
4.
5.
6.