Lesson 2.5 AIM: Proving Angles Congruent

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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

4x and 3x + 5 are vertical angles. Find the value of x.
4x = 3x + 5 -3x -3x x = 5 4x (3x + 5)

(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

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

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

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

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

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

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

Summary Question Define vertical angles. Define supplementary angles.
Define complimentary angles.