Question

Prove that alternate interior angles 3 and 6 are congruent.Is there another answer to it

Answer 1

Let us suppose that lines m and n are parallel lines and a transversal line intersects these parallel lines.

We know that whenever any transversal line intersects two parallel lines then corresponding angles and vertical angles are congruent (equal).

From the figure, we see that angle 2 and angle 6 are corresponding angles.

$\angle2=\angle6\qquad \text{corresponding angles}$

From the figure, we see that angle 2 and angle 3 are vertical angles.

$\angle2=\angle3\qquad \text{vertical angles}$

Therefore, from the above two relations, we see that

$\angle3=\angle6\qquad \text{alternate interior angles}$