To prove that quadrilateral ABCD is a parallelogram, we can use one of several properties that confirm a shape is a parallelogram. Hereβs a quick overview of some of these properties:
1. **Opposite sides are parallel**: If both pairs of opposite sides of a quadrilateral are parallel, then the quadrilateral is a parallelogram.
2. **Opposite sides are congruent**: If both pairs of opposite sides are congruent, the quadrilateral is a parallelogram.
3. **Opposite angles are congruent**: If both pairs of opposite angles are congruent, the quadrilateral is a parallelogram.
4. **Diagonals bisect each other**: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
5. **One pair of opposite sides is both parallel and congruent**: If one pair of opposite sides of a quadrilateral are both parallel and congruent, the quadrilateral is a parallelogram.
Given your options, hereβs how we can confirm the proof based on the appropriate property:
- If **opposite sides of the figure are congruent**, then quadrilateral ABCD is indeed a parallelogram.
So, in response to how you know that the figure is a parallelogram, the correct response would be:
**Opposite sides of the figure are congruent.**