Question

in parallelogram abcd, diagonals $overline{ac}$ and $overline{bd}$ intersect at e.
which statement proves abcd is a rectangle?

1. $overline{ac} cong overline{bd}$
2. $overline{ad} perp overline{bd}$
3. $overline{ac} perp overline{bd}$
4. $overline{ac}$ bisects $angle bcd$

Explanation:

A parallelogram is a rectangle if its diagonals are congruent.

• Option 2: $\overline{AD} \perp \overline{BD}$ would mean the parallelogram is a right parallelogram but this condition does not universally prove it is a rectangle.
• Option 3: $\overline{AC} \perp \overline{BD}$ proves the parallelogram is a rhombus, not a rectangle.
• Option 4: $\overline{AC}$ bisects $\angle BCD$ proves the parallelogram is a rhombus, not a rectangle.

Only congruent diagonals confirm a parallelogram is a rectangle.

Answer:

1. $\overline{AC} \cong \overline{BD}$