1. 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

2. 4x and 3x + 5 are vertical angles. Find the value of x.
4x = 3x + 5
-3x -3x
x = 5 4x
(3x + 5)

3. (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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

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