1. We will apply properties of perpendicular1 bisectors2 of a triangle to find missing angles and sides.
LEARNING OBJECTIVE
Declare the Objective
A: Read the objective to B.
B: Define perpendicular and bisectors
Definition
1 Form an angle of 90° to a given line.
2 Cuts an object into two equal parts.

2. ACTIVATE PRIOR KNOWLEDGE
Remember the Concept
Angle Bisector Theorem-Cuts an angles into two equal parts & sides.
Find the measure BC 1 2
Make the Connection
Students, you already know how to find the missing sides. Now, we are going to prove and apply theorems about angle bisectors
ACTIVATE PRIOR KNOWLEDGE

4. Example
Since a triangle has three sides, it has three perpendicular bisectors.
CONCEPT DEVELOPMENT
The circumcenter can be inside the triangle, outside the triangle, or on the triangle.
Check for Understanding
In your own words, what is Circumcenter of Triangle and what does it states?
“A circumcenter of a Triangle is______”

5. Check for Understanding
B Explain to A: What is the Angle Bisector Theorem states?

6. Find the measure: m∠JKL
Find mMKL
Find the measure: m∠JKL
Remember the Concept
Def. of  bisector
CONCEPT DEVELOPMENT
mMKL = mJKM
3a + 20 = 2a + 26
Def. of  bisector
a + 20 = 26
a = 6
-3x x -2
So mMKL = [2(6) + 26]° = 38°
-x = -10
Check for Understanding
A Explain to B: How did we find the mMKL?
x = 10

7. Find the measure m∠LJM,
given that m∠KJM = 28°
Find the measure m∠ LKM,
given that m∠ JKL = 57°.

9. ?
Check for Understanding
A Explain to B: How did we find the mPQX?

11. What did you learn today about how to apply properties of perpendicular bisectors of a triangle to find the missing angles and sides?
Word Bank
Circumcenter of a triangle
Circumscribed
Incenter of a triangle
SUMMARY CLOSURE