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**Lesson 2.5 AIM: Proving Angles Congruent**

Do Now: Name the property illustrated. XY = XY Reflexive Property b. If a = b and b = c then a = c Transitive Property c. If x = y then y = x Symmetric property

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**4x and 3x + 5 are vertical angles. Find the value of x.**

4x = 3x + 5 -3x -3x x = 5 4x (3x + 5)

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**(5x – 20) and (3x + 8) are vertical angles**

(5x – 20) and (3x + 8) are vertical angles. (5x + 4y) and (5x – 20) are supplementary angles. Find x and y. Solve for x. 5x - 20 = 3x + 8 -3x x 2x - 20 = 8 2x = 28 x = 14 (5x - 20) (3x + 8) (5x + 4y) Solve for y. 5x + 4y + 5x - 20 = 180 5(14) + 4y + 5(14) -20 = 180 70 + 4y = 180 4y +120 = 180 4y = 60 y = 15

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**STATEMENT JUSTIFICATION**

Angle 1 and Angle 3 are Complementary. Angle 2 and Angle 3 are Complementary. Prove Angle 1 is Congruent to Angle 2. STATEMENT JUSTIFICATION

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**STATEMENT JUSTIFICATION**

Angle 1 and Angle 3 are Complementary. Angle 2 and Angle 3 are Complementary. Prove Angle 1 is Congruent to Angle 2. STATEMENT A 1 + A 3 = 90 JUSTIFICATION 1. Definition of Complementary

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**STATEMENT JUSTIFICATION**

Angle 1 and Angle 3 are Complementary. Angle 2 and Angle 3 are Complementary. Prove Angle 1 is Congruent to Angle 2. STATEMENT A 1 + A 3 = 90 A 2 + A 3 = 90 JUSTIFICATION 1. Definition of Complimentary 2. Definition of Complimentary

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**STATEMENT JUSTIFICATION**

Angle 1 and Angle 3 are Complementary. Angle 2 and Angle 3 are Complementary. Prove Angle 1 is Congruent to Angle 2. STATEMENT A 1 + A 3 = 90 A 2 + A 3 = 90 A 1 + A 3 = A 2 + A 3 JUSTIFICATION 1. Definition of Complimentary 2. Definition of Complimentary Substitution Property

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**STATEMENT JUSTIFICATION**

Angle 1 and Angle 3 are Complementary. Angle 2 and Angle 3 are Complementary. Prove Angle 1 is Congruent to Angle 2. STATEMENT A 1 + A 3 = 90 A 2 + A 3 = 90 A 1 + A 3 = A 2 + A 3 - A A 3 JUSTIFICATION 1. Definition of Complimentary 2. Definition of Complimentary Substitution Property

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**STATEMENT JUSTIFICATION**

Angle 1 and Angle 3 are Complementary. Angle 2 and Angle 3 are Complementary. Prove Angle 1 is Congruent to Angle 2. STATEMENT A 1 + A 3 = 90 A 2 + A 3 = 90 A 1 + A 3 = A 2 + A 3 - A A 3 A = A2 JUSTIFICATION 1. Definition of Complimentary 2. Definition of Complimentary Substitution Property Subtraction Property of Equality

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**Summary Question Define vertical angles. Define supplementary angles.**

Define complimentary angles.

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