Question

Which plan for a proof for this problem will show that quadrilateral abdc is a parallelogram?

1) Plan A: Prove that opposite sides are parallel
2) Plan B: Prove that opposite angles are congruent
3) Plan C: Prove that diagonals bisect each other
4) Plan D: Prove that opposite sides are congruent

Answer 1

Any one of the properties listed—opposite sides being parallel, opposite angles being congruent, diagonals bisecting each other, or opposite sides being congruent—is sufficient to prove that quadrilateral ABDC is a parallelogram.

Step-by-step explanation:

To determine if quadrilateral ABDC is a parallelogram, one could use any of the following characteristics of a parallelogram as proof:

1. Show that opposite sides are parallel (Plan A).
2. Show that opposite angles are congruent (Plan B).
3. Show that the diagonals bisect each other (Plan C).
4. Show that opposite sides are congruent (Plan D).

In a parallelogram, any one of these properties is sufficient to establish that a quadrilateral is a parallelogram. Therefore, any of these plans can be used as a valid proof strategy.