Question

54 points!!!!!!!explainGiven: Parallelogram ABCD, AB = AD, and

AC⊥BD

. Which statement can be proved?


A.

ABCD is a rectangle, but not necessarily a square.


B.

ABCD is a parallelogram, but not necessarily a rhombus.


C.

ABCD is a rhombus, but not necessarily a square.


D.

ABCD is a square.

Answer 1

C. ABCD is a rhombus, but not necessarily a square.

Explanation:

A parallelogram with adjacent sides congruent is a rhombus, which also happens to have perpendicular diagonals (that bisect each other). If the diagonals are different length, then the parallelogram is not a rectangle, so the rhombus is not a square.