Question

How do you prove corresponding angles are equal?

Answer 1

Suppose you have two parallel lines cut by a transversal.

Due to the straight angle (linear pair) theorem, we know that

`{(mangle2+mangle3=180˚),(mangle5+mangle6=180˚):}`

Thought the transitive property, we can say that

`mangle2+mangle3=mangle5+mangle6color(white)(xxxx)` (1)

Though the alternate interior angles theorem, we know that

`mangle3=mangle5`

Use substitution in (1):

`mangle2+mangle3=mangle3+mangle6`

Subtract `mangle3` from both sides of the equation

`mangle2=mangle6`

`thereforeangle2congangle6`

Thus `angle2` and `angle6` are corresponding angles and have proven to be congruent.