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 = [tex]360^{o}[/tex] (sum of angles at a point)
Also,
<5 + <6 + <7 + <8 = [tex]360^{o}[/tex] (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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