Section 5.2- Perpendicular and Angle Bisectors
Essential Question: What is the special relationship between points on perpendicular
bisectors and angle bisectors?
What type of triangle is formed?
NOTE: Theorem 5-3 states the SAME THING as a ____________ bisector in an
_________________ triangle in Section 4-5.
Example 1: Using the Perpendicular Bisector Theorem
̅̅̅̅?
What is the length of 𝑄𝑅
Use the TI-Nspire Demo to help you complete the blanks in the following theorems.
Example 2: Using the Angle Bisector Theorem
̅̅̅̅?
What is the length of 𝐹𝐵
Group Work:
1. What is the relationship between ̅̅̅̅
𝐴𝐶 and ̅̅̅̅
𝐵𝐷?
2. What is the length of ̅̅̅̅
𝐴𝐵 ?
̅̅̅̅ ?
3. What is the length of 𝐷𝐶
(8 steps)
Statements
⃗⃗⃗⃗⃗ , ̅̅̅̅
⃗⃗⃗⃗⃗
1. ⃗⃗⃗⃗⃗
𝑄𝑆 bisects ∠𝑃𝑄𝑅, ̅̅̅̅
𝑆𝑃 ⊥ 𝑄𝑅
𝑆𝑅 ⊥ 𝑄𝑅
Reasons
1.
(8 steps)
Statements
⃗⃗⃗⃗⃗ , ̅̅̅̅
⃗⃗⃗⃗⃗ , SP=SR
1. ̅̅̅̅
𝑆𝑃 ⊥ 𝑄𝑅
𝑆𝑅 ⊥ 𝑄𝑅
HW: p. 296-298 #6-8, 12-22, 29-31
Reasons
1.