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.