Question

prove the alternate exterior angles theorem

Answer 1

Ok, so

Given the figure:

Given that:

$p\mleft\Vert q\mright?$

If parallel lines are cut by a transversal, then their corresponding angles are congruent. So we have that:

$\angle a\cong\angle b$

Then, if two angles are vertical angles, then they are congruent. So,

$\angle b\cong\angle c$

Now, by transitive property, if two angles are congruent to the same angle, then they are congruent. Then,

$\angle a\cong\angle c$

Hance proved, the alternate exterior angles theorem.