Page 3 - AG Unit 2 Capacity, Cavalieri, and Constructions

AG
2.1 A Angle Bisectors, Perpendicular Bisector Properties and Constructions

Name ________________________________________ Date ____________ Class _____
1. Angle bisectors of a triangle extend from ____________________ to _______________.
2. The point of concurrency for angle bisectors is called ____________________.
3. Incenters are equidistant to what part of a triangle? _______________
4. Why is the point called an incenter? __________________________________

_____________________________________________________________________

5. List the steps to create an incenter when given a triangle.
a.
b.
c.
d.
e.
6. List similarities and differences between angle bisectors and perpendicular bisectors.

7. What is the point of concurrency for perpendicular bisectors?

8. State the relationship between the circumcenter and the type of triangle it relates to.
Hint: obtuse, right, acute . . . .

9. List the steps to create a circumcenter when given the triangle.

a.
b.
c.
d.
e.

Incenters

10. Is the incenter of an obtuse triangle inside, outside, or on the triangle?
11. Can the incenter and the circumcenter of a triangle ever be the same point?
12. and are angle bisectors of ⊿PQR, and ∡PIR =130°.
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a. Given ⊿RPQ =30°, find ∡PRT, ∡ PRQ, and ∡Q.
b. Given ⊿RPQ =50°, find ∡PRT, ∡ PRQ, and ∡Q.
13. If and are congruent, what is the measure of ∡RQI? You may use an
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algebraic expression as your response.