If diagonal DB is congruent to each side of rhombus ABCD, what is the measure of ∠A? Of ∠ABC?

Question

1. If diagonal DB is congruent to each side of rhombus ABCD, what is the measure of ∠A? Of ∠ABC?
2. If the diagonals of a parallelogram are perpendicular, what can you conclude about the parallelogram?

Answer 1

No, Mark, my immediate reaction was the same as yours...but it's wrong.

If a diagonal of a rhombus is equal (congruent) to a side, then the rhombus is made up of 2 equilateral triangles and two of the angles are each 60° and the other 2 are 120°.

If the diagonals are perpendicular, then the rhombus is a square.