In the given figure, line m is parallel to line n, and line a is parallel to line b.

Corresponding angles are two or more angles that have similar properties. Thus they have equal measures.

The required prove is given in the explanation below:

Considering the given diagram, it can be observed that:

<1 ≅ <3 and <2 ≅ <4     (vertically opposite angle theorem)

Also,

<5 ≅ < 7 and <6 ≅ <8    (vertically opposite angle theorem)

m ⊥ n and a ⊥ b             (given)

Thus,

<1 + <2 + <3 + <4 = (sum of angles at a point)

Also,

<5 + <6 + <7 + <8 =  (sum of angles at a point)

Therefore,

<1 ≅ <7                             (corresponding exterior angle property)

Therefore by corresponding exterior angle theorem, <1 ≅ <7.

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vertical angles theorem

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