Question

Name each of the following parallelograms.
(i) The diagonals are equal and the adjacent sides are unequal.
(ii) The diagonals are equal and the adjacent sides are equal.
(iii) The diagonals are unequal and the adjacent sides are equal.
(iv) All the sides are equal and one angle is 60°.
(v) All the sides are equal and one angle is 90°.
(vi) All the angles are equal and the adjacent sides are unequal.

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{The}\mathrm{diagonals}\mathrm{are}\mathrm{equal}\mathrm{and}\mathrm{the}\mathrm{adjacent}\mathrm{sides}\mathrm{are}\mathrm{unequal}. \\ \mathrm{Hence},\mathrm{the}\mathrm{given}\mathrm{parallelogram}\mathrm{is}\mathrm{a}\mathrm{rectangle}. \\ \left(\mathrm{ii}\right)\mathrm{The}\mathrm{diagonals}\mathrm{are}\mathrm{equal}\mathrm{and}\mathrm{the}\mathrm{adjacent}\mathrm{sides}\mathrm{are}\mathrm{equal}. \\ \mathrm{Hence},\mathrm{the}\mathrm{given}\mathrm{parallelogram}\mathrm{is}\mathrm{a}\mathrm{square}. \\ \left(\mathrm{iii}\right)\mathrm{The}\mathrm{diagonals}\mathrm{are}\mathrm{unequal}\mathrm{and}\mathrm{the}\mathrm{adjacent}\mathrm{sides}\mathrm{are}\mathrm{equal}. \\ \mathrm{Hence},\mathrm{the}\mathrm{given}\mathrm{parallelogram}\mathrm{is}\mathrm{a}\mathrm{rhombus}. \\ \left(\mathrm{iv}\right)\mathrm{All}\mathrm{the}\mathrm{sides}\mathrm{are}\mathrm{equal}\mathrm{and}\mathrm{one}\mathrm{angle}\mathrm{is}60°. \\ \mathrm{Hence},\mathrm{the}\mathrm{given}\mathrm{parallelogram}\mathrm{is}\mathrm{a}\mathrm{rhombus}. \\ \left(\mathrm{v}\right)\mathrm{All}\mathrm{the}\mathrm{sides}\mathrm{are}\mathrm{equal}\mathrm{and}\mathrm{one}\mathrm{angle}\mathrm{is}90°. \\ \mathrm{Hence},\mathrm{the}\mathrm{given}\mathrm{parallelogram}\mathrm{is}\mathrm{a}\mathrm{square}. \\ \left(\mathrm{vi}\right)\mathrm{All}\mathrm{the}\mathrm{angles}\mathrm{are}\mathrm{equal}\mathrm{and}\mathrm{the}\mathrm{adjacent}\mathrm{sides}\mathrm{are}\mathrm{unequal}. \\ \mathrm{Hence},\mathrm{the}\mathrm{given}\mathrm{parallelogram}\mathrm{is}\mathrm{a}\mathrm{rectangle}. \end{gathered}$$