Corresponding Angles Theorem (Postulate): If a transversal intersects two parallel lines, then corresponding angles are congruent.
Given: Line AB is parallel to line CD
Prove: Angle CGE and angle AHE are congruent
Statements:
1. AB is parallel to line CD
2. Points E, G, H, F fall all on the same line
3. The measure of angle EGF is equal to 180 degrees
4. The measure of angle CGE + the measure of angle CGF = the measure of angle EGF
5. The measure of angle CGE + the measure of angle CGF = 180 degrees
6. The measure of angle AHE + the measure of angle CGF = 180 degrees
7. The measure of angle CGE + the measure of angle CGF = the measure of angle AHE + the measure of angle CGF
8. The measure of angle CGE + the measure of angle CGF – the measure of angle CGF = the measure of angle AHE + the measure of angle CGF – the measure of angle CGF
9. Angle CGE is congruent to angle AHE
Reasons:
1. Given
2. Given
3. Definition of Straight Angle
4. Angle Addition Postulate
5. Substitution Property of Equality
6. Same-Side Interior Angles Theorem
7. Substitution Property of Equality
8. Subtraction Property of Equality
9. Definition of Congruency
