Question

state and prove alternate angle therom​

Answer 1

Answer:

The Alternate Interior Angles Theorem

Given: a//d

To prove: ∠4 = ∠5 and ∠3 = ∠6

Proof: Suppose a and d are two parallel lines and l is the transversal which intersects a and d at point P and Q.

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent . So, in the figure below, if k∥l , then ∠2≅∠8 and ∠3≅∠5 .

Statement: The theorem states that “ if a transversal crosses the set of parallel lines, the alternate interior angles are congruent”.

Answer 2

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent . So, in the figure below, if k∥l , then ∠2≅∠8 and ∠3≅∠5 . Proof.