Compare parallelograms, rectangles, rhombuses, and squares — learning what properties make each one unique.
In a parallelogram, opposite sides are equal and parallel, opposite angles are equal, and the diagonals bisect each other (cut each other exactly in half).
In parallelogram ABCD, angle A = 70°. Find angle C (the opposite angle).
70°, since opposite angles in a parallelogram are equal
In parallelogram ABCD, angle A = 70°. Find angle B (an adjacent angle).
180° − 70° = 110°, since adjacent angles in a parallelogram are supplementary
A rectangle is a parallelogram with all angles 90°. A rhombus is a parallelogram with all sides equal. A square is both — a parallelogram with all angles 90° AND all sides equal.
What makes a rhombus different from a general parallelogram?
In a rhombus, all four sides are equal in length, which isn't required in a general parallelogram
Why is every square also a rectangle, but not every rectangle a square?
A square meets all the requirements of a rectangle (all angles 90°) plus the extra requirement of equal sides, while a rectangle only needs equal angles
1. In parallelogram PQRS, angle P = 65°. Find angle R.
2. In parallelogram PQRS, angle P = 65°. Find angle Q.
3. A rhombus has a diagonal that bisects it. What special property do the diagonals of a rhombus have, beyond bisecting each other?
4. Is every rhombus a square? Explain.
5. A parallelogram has all four sides equal and all four angles equal to 90°. What shape is it?