Properties of Quadrilaterals Worksheet

Sample problems

Use the defining properties of each shape. In a parallelogram, opposite sides and opposite angles are equal, consecutive angles are supplementary, and the diagonals bisect each other. A rectangle adds equal diagonals; a rhombus adds four equal sides and perpendicular diagonals. The four angles of any quadrilateral sum to $360^{\circ }$. Show your reasoning.

1. 1. In a parallelogram, one angle measures $110^{\circ }$. Find the measure $x$ of an angle next to it (a consecutive angle).
2. 2. In a parallelogram, one angle measures $72^{\circ }$. Find the measure $x$ of the angle opposite it.
3. 3. The four angles of a quadrilateral measure $85^{\circ }$, $95^{\circ }$, $110^{\circ }$, and $x^{\circ }$. Find $x$.
4. 4. A rhombus has a perimeter of $52$. Find the length of one side.

Plus 11 more problems and a full answer key in the PDF.