Prove If two parallel lines are cut by a transversal then th

Prove If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Given: m and n are parallel lines.

To Prove: Corresponding angles are equal.

Proof:
We are given with two parallel lines.

2 = 6 (Corresponding angles). Hence proved.

Similarly, this can be proven for every pair of corresponding angles.

	Statement	Reason
Step 1	m \|\| n	Given
Step 2	2 + 3 = 180	2 is supplementary to 3 (Straight Angle Theorem)
Step 3	5 + 6 = 180	5 is supplementary to 6 (Straight Angle Theorem)
Step 4	2 + 3 = 5 + 6	From Step 2 and Step 3
Step 5	3 = 5	Alternate Interior Angle Theorem
Step 6	2 = 6	Using Step 5 in Step 4