Given quadrilateral ABCD, where ∠A≅∠C and ∠B≅∠D. Can you prove can you prove that the figure is a parallelogram? Explain.

Question

Given quadrilateral ABCD, where ∠A≅∠C and ∠B≅∠D. Can you prove can you prove that the figure is a parallelogram? Explain.

1. A. Yes; opposite angles are congruent.
2.  B. No; you cannot prove that the quadrilateral is a parallelogram.
3.  C. Yes; opposite sides are congruent.
4.  D. Yes; two opposite sides are both parallel and congruent.

Answer 1

Proof:

because the opposite angles are congruent, the opposite sides are parallel.

That is AB is parallel to CD and AD is parallel to BC

Drawing the diagonal DB, angles ADB = angle DBC and angle BDC = angle DBA

side DB =side BD by reflexive property.

So triangle ADB is congruent to triangle CBD.

So AB = CD and AD = BC by CPCTC.

So the opposite sides are congruent and parallel