2. 2-6 Proving Angles Congruent
To prove and apply theorems about angles

6. 3x = 2x + 40 Vertical Angles Theorem
x = 40 Subtraction Property of =

12. Proof of Congruent Supplements Theorem
COMPLEMENTS
complementary
complementary
Proof:
By the definition of supplementary angles, m∠1 + m ∠ 2 = 180 and m ∠ 3 + m ∠ 2 = 180.
By transitive property of equality, m ∠1 + m ∠ 2=m ∠3 + m ∠2
Subtract m ∠ 2 from each side. You get m ∠1=m ∠3, or ∠1≌∠3
complementary 90 90

13. Prove: All right angles are congruent
Given: ∠1 and ∠2 are right angles.
Prove: ∠1 ≌ ∠2
Proof:
By the definition of right angle, m∠1 = 90 and m∠2 = 90.
By transitive property of equality, m∠1 = m∠2, or ∠1 ≌ ∠2.

14. Prove: If two angles are congruent and supplementary, then each angle is a right angle.
Proof:
∠W and ∠ V are congruent, so m ∠W = m ∠V.
∠W and ∠V are supplementary so m ∠ W + m ∠ V = 180.
Substituting m ∠W for m ∠V, you get m ∠W + m ∠W = 180, or 2m ∠W = 180.
By the Division Property of Equality, m ∠ W = 90.
Since ∠ W ≌ ∠ V, m ∠ V = 90, too.
Then both angles are right angles.

15. 2-6 Quiz
The following questions are designed to help you determine how well you understood today’s lesson. See me if you don’t understand what you miss…
Remember to record how many you get right on your portfolio.

16. 1. Supplementary angles are two angles whose measures have sum ____
1. Supplementary angles are two angles whose measures have sum ____. Complementary angles are two angles whose measures have sum ____.
90; 180
90; 45
180; 360
180; 90
Non-Response Grid

17. Non-Response Grid

18. 3. complementary angles; Transitive right angles; Transitive
complementary angles; Reflexive
right angles; Symmetric
Non-Response Grid

19. 4. Find the value of x. 19
125
-19 55
Non-Response Grid

20. 5. Find the values of x and y.
x = 112, y = 68
x = 68, y = 112
x = 15, y = 17
x = 17, y = 15
Non-Response Grid

21. Assignment
2-6 p #6-30 even