Question

prove corresponding angle axiom

Answer 1

Given: m and n are parallel lines.

To Prove: Corresponding angles are equal.

Proof:
We are given with two parallel lines.

StatementReason
Step 1 
m || n

Step 2 
∠∠2 + ∠∠3 = 180oo.
∠∠2is supplementary to ∠∠3(Straight AngleTheorem)

Step 3∠∠5 + ∠∠6 = 180oo∠∠5 is supplementary to ∠∠6
(Straight AngleTheore)

Step 4∠∠2 + ∠∠3 = ∠∠5 + ∠∠6From Step 2 and Step 3

Step 5∠∠3 = ∠∠5Alternate Interior AngleTheorem


Step 6∠∠2 = ∠∠6Using Step 5 in Step 4
∴∴ ∠∠2 = ∠∠6 (Corresponding angles). Hence proved.

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