1. Find the measure of each numbered angle and name the theorem that justifies your work.
Problem of the Day

2. Section 2-8b Proving Angle Relationships

3. Then
Now
Objectives
You wrote proofs involving supplementary and complementary angles.
Write proofs involving congruent and right angles.

4. Common Core State Standards
Content Standards
G.CO. 9 – Prove theorems about lines and angles.
Mathematical Practices
3) Construct viable arguments and critique the reasoning of others.
6) Attend to precision.
Common Core State Standards

5. Properties of Angle Congruence

6. Theorems

7. Given: ∠9 and ∠10 are comp. ∠8 and ∠9 are comp
Given: ∠9 and ∠10 are comp. ∠8 and ∠9 are comp. m∠8 = 41 Prove: m∠10 = 41
Example 3

8. Given: ∠1 and ∠2 are supp. ∠2 and ∠3 are supp
Given: ∠1 and ∠2 are supp. ∠2 and ∠3 are supp. m∠3 = 78 Find: m∠1 and m∠2 (Name the theorems you used to justify your work.)
Example 3

9. Vertical Angles Theorem

10. If ∠3 and ∠4 are vertical angles, m∠3 = 6x + 2, and m∠4 = 8x – 14, find m∠3 and m∠4. Justify each step.
Example 4

11. If ∠1 and ∠2 are vertical angles, m∠1 = d – 32, and m∠2 = 175 – 2d, find m∠1 and m∠2. Justify each step.
Example 4

12. Right Angle Theorems

13. p.156 #7, 8-10, 12, 41-44
Homework

14. If m∠A = 5x – 12, m∠B = 2x + 18, ∠A and ∠C are supplementary, and ∠B and ∠C are supplementary, find m∠C.
Problem of the Day