Question

If ABCD is a parallelogram, which statement wouldprove that ABCD is a rhombus?1) ZABC = ZCDA 2) AC = BD3) AC I BD 4) AB I CDChoose

Answer 1

Answer: 1.

`\measuredangle ABC\cong\measuredangle CDA`

Step by step solution:

In a parallelogram, the opposite sides are parallel and equal. Not all his sides are equal just opposite sides.

In a Rhombus, all sides are equal and the opposite sides are parallel.

The above figure is a rhombus ABCD.

Now we know that the ABCD parallelogram is a rhombus if: Angle ABC is congruent (equal) to angle CDA

`\measuredangle ABC\cong\measuredangle CDA`