Question

Which of the following information is sufficient for constructing a rhombus?

• A. $\angle PQR={120}^o$ and all sides are equal
• B. $\angle PQR={110}^o$ and $\angle QRS={70}^o$
• C. None of the above
• D. $\angle PQR={130}^o$ and one of the sides = 5 cm

Answer 1

The correct option is D $\angle PQR={130}^o$ and one of the sides = 5 cm

We can construct a rhombus when one of the angles and a side are known.

Since a rhombus has all sides equal, one measure of length is sufficient.
Also, the measure of the adjacent angles of a parallelogram add up to ${180}^o$.
So, knowing one angle is also sufficient.

Hence, out of the given options, a rhombus can be constructed using the measurements $\angle PQR={130}^o$ and one of the sides = 5 cm.