Edwidge draws a parallelogram STUV with a center at O. What must be true to prove that STUV is a parallelogram?

Question

a. SO ≅ TO and UO ≅ VO
b. ST ≅ TU and UV ≅ SV
c. ST ≅ UV and TU ≅ SV
d. SO ≅ VO and TO ≅ UO

Answer 1

To prove that STUV is a parallelogram, you need to show that either one pair of opposite sides is equal and parallel or the diagonals bisect each other.

In the context of this question, option d. SO ≅ VO and TO ≅ UO indicates that the diagonals (SU and TV, which go through the center O) bisect each other. This is a property of parallelograms, where the diagonals bisect each other at the midpoint of both diagonals and confirms that STUV is a parallelogram.

So, the correct answer is:

d. SO ≅ VO and TO ≅ UO.