1. Table of Contents
Date: Topic: Description: Page:

2. Section 5.1 : Bisectors of Triangles

3. Perpendicular Bisector:
Vocabulary:
Segment Bisector:
 A segment that cuts
another segment into
two congruent halves
Perpendicular Bisector:
A segment bisector
that ALSO cuts the
segment at a 90 angle.

4. Vocabulary: perpendicular bisector of a segment, then that point is
 Perpendicular Bisector Theorem:
 If a point is on the
perpendicular bisector
of a segment, then that point is
equidistant from the
endpoints of the bisected segment.
Converse of the Perpendicular Bisector Theorem:
If a point is equidistant from
the endpoints of the segment,
then it is on the perpendicular
bisector of a segment.

5. Example 1: a) Find the length of BC.
What type of relationship should I use in order to find the length of BC?

6. Example 1: b) Find the length of XY.
How is this diagram different to the previous diagram?

7. Example 1:
c) Find the length of PQ.

8. Vocabulary: intersect at a common point. concurrent lines intersect.
 Concurrent Lines:
 When 3 or more lines
intersect at a common point.
Point of Concurrency:
 The point where the
concurrent lines intersect.

9. Vocabulary: of a triangle intersect at a point called the circumcenter
 Circumcenter Theorem
 The perpendicular bisectors
of a triangle intersect at a
point called the circumcenter
that is equidistant from
the vertices.

10. Example 2:
A triangular-shaped garden is shown. Can a fountain be placed at the circumcenter and still be inside the garden?

11. Angle Bisector Theorem:
Vocabulary:
 Angle Bisector
 A segment that cuts
an angle into two
halves.
Angle Bisector Theorem:
 If a point on the bisector
of an angle, then it is
equidistant from the
sides of the angle.   

12. Converse of the Angle Bisector Theorem:
Vocabulary:
 Converse of the Angle Bisector Theorem:
 If a point in the interior of an angle
is equidistant from the sides of an angle,
then it is an angle bisector.

13. Example 3: a) Find the length of DB.
What conclusion can be made if given a segment is an angle bisector?

14. Example 3: b) Find measure of angle WYZ.
What conclusions can be made if given the two segments from the angle bisector are equal and intersect at a right angle?

15. Example 3: c) Find the length of QS.
Given the set up to the right, what can I do to my two expressions? And why?

16. Vocabulary: The point of concurrency Incenter:
Incenter:
 The point of concurrency
of the Angle bisectors of a triangle.
Incenter Theorem:
 The angle bisectors of a
triangle intersect at a point
called the incenter that is
equidistant from the sides of the triangle.

17. Example 4: Find ST if S is the incenter of ΔMNP.
Find mSPU if S is the incenter of ΔMNP.
If S is the incenter, what do I know about my triangle?

18. Summary!
1) Find the value of x ) Find the length of KL.

19. Summary!
3) Find 𝑚∡𝐿𝑌𝐹 4) Point A is the incenter of ∆𝑃𝑄𝑅 Find the measure of ∡𝑄𝑃𝐾.