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

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

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

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.

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.

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.

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

    Non-Response Grid

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

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

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

Assignment 2-6 p. 124-126 #6-30 even