Proving a Quadrilateral is a Parallelogram | Proofs & Examples Video - Free Printable

Let’s think about what makes a quadrilateral a parallelogram.

A parallelogram is a four-sided shape (quadrilateral) where:
- Opposite sides are parallel.
- Opposite angles are equal.
- Consecutive angles add up to 180 degrees (they’re supplementary).
- The diagonals bisect each other (but we don’t need that here).

In the diagram, we see arrows on the sides — those mean “parallel.” So top and bottom have double arrows → they’re parallel. Left and right have single arrows → they’re also parallel. That already tells us it’s a parallelogram by definition!

But let’s look at the angles too — just to be sure.

We see two pink arcs and two blue arcs. In geometry diagrams, same-colored arcs mean those angles are equal.

So:
- The two pink angles are opposite each other → they should be equal in a parallelogram ✔
- The two blue angles are opposite each other → they should also be equal ✔

Also, notice: one pink angle and one blue angle are next to each other (consecutive). In a parallelogram, consecutive angles must add up to 180°. Since the diagram shows them as different colors, they’re likely meant to be different measures — which fits with being supplementary.

Everything matches the rules for a parallelogram.

✔ Opposite sides are parallel (shown by arrows)
✔ Opposite angles are equal (same color = same measure)
✔ Consecutive angles are supplementary (different colors, so probably not equal — which is correct)

So yes — this quadrilateral IS a parallelogram.

Final Answer: Yes, the quadrilateral is a parallelogram because both pairs of opposite sides are parallel and opposite angles are equal.