If angles are supplementary to congruent angles then the are congruent to each other.

GIVEN:Ð 1 is supplementary to Ð 2

Ð 2 @ Ð 4

PROVE: Ð 1 @ Ð 3

IF

THEN

REASONS

1. ---------------------

Ð 1 is supplementary to Ð 2

1. Given

2.Ð 1 is supplementary to Ð 2

mÐ 1 + mÐ 2 = 180°

2. Def of Supplementary Ð 's

3. ---------------------

Ð 3 is supplementary to Ð 4

3. Given

4. Ð 3 is supplementary to Ð 4

mÐ 3 + mÐ 4 = 180°

4. Def of Supplementary Ð 's

mÐ 1 + mÐ 2 = 180°

5. mÐ 3 + mÐ 4 = 180°

mÐ 1 + mÐ 2 = mÐ 3 + mÐ 4

5. Substitution

6. ---------------------

Ð 2 @ Ð 4

6. Given

7. Ð 2 @ Ð 4

mÐ 2 = mÐ 4

7. Definition of Congruent Ð 's

mÐ 1+ mÐ 2=mÐ 3+mÐ 4

8. mÐ 2 = mÐ 4

mÐ 1 + mÐ 2 = mÐ 3 + mÐ 2

8. Substitution

9. mÐ 1+mÐ 2=mÐ 3+mÐ 2

mÐ 1 + mÐ 2 = mÐ 3 + mÐ 2

- mÐ 2 - mÐ 2

9. Subtraction

10. mÐ 1+mÐ 2=mÐ 3+mÐ 2

- mÐ 2 - mÐ 2

mÐ 1 + 0 = mÐ 3 + 0

11. mÐ 1 + 0 = mÐ 3 + 0

mÐ 1 = mÐ 3

11. Identity Property

12. mÐ 1 = mÐ 3

Ð 1 @ Ð 3

12. Definition of Congruent Ð 's