Question

State whether the following axioms are True or False:

If a transversal intersect two parallel lines, then alternate interior angles are equal.

• A. True
• B. False
• C. Ambiguous
• D. None of these

Answer 1

The correct option is A True

If a transversal intersect two parallel line then alternate interior angles are equalis true.

We can prove it by using converse of the corresponding angles axiom which states .

"If a transversal intersects two lines such that a pair of corresponding angles is equal then the two lines are parallel to each other."

$\angle BQR=\angle CRQ$ (alt. angles)

let us assume they are equal show AB||CD

$\angle BQR=\angle PQA$--------------------1 (vertically opposite angle)

$\angle BQR=\angle QRC$ -------------------2 (assumed)

so from 1 and 2$\angle PQA=\angle QRC$

as they are corresponding angles

so, $AB||CD$ {converse of corresponding angle axiom}