Question

Given: line AD parralell to line BC and line AB is parralell to line CD. prove Line AV is congruent CD.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To prove that line AV is congruent to CD, we can use the fact that AB is parallel to CD and line AD is parallel to BC.

Let's label the intersection point of lines AB and CD as E, and the intersection point of lines AD and BC as F.

Since AB is parallel to CD, we have ∠BAE = ∠CED (alternate interior angles).

Also, since AD is parallel to BC, we have ∠ADF = ∠BFC (alternate interior angles).

Now, consider triangle ABE and triangle CED. We have:

∠BAE = ∠CED (as we established earlier)
∠B = ∠C (corresponding angles)
AB = CD (given, resulting from parallel lines)

By angle-angle-side (AAS) congruence, we can conclude that triangle ABE is congruent to triangle CED.

Since triangle ABE is congruent to triangle CED, we have AV = CD (corresponding sides of congruent triangles).

Therefore, line AV is congruent to CD.