Question

Different types of parallelograms have distinguishing traits. Compare and contrast the rectangle, rhombus, and square based upon the characteristics of their angles. Which one(s) have angles whose sum is 360? Which one(s) have both pairs of opposite angles that are congruent? Which one(s) have four right angles

Answer 1

A parallelogram is a simple quadrilateral with two pairs of parallel sides.

1. Parallelogram which have angles whose sum is 360 degree:

Rectangle is a quadrilateral whose each angle is a right angle.

Therefore Sum of all 4 angles =
`4 * 90 = 360` degrees.

Square is a quadrilateral whose each angle is a right angle.

Therefore, Sum of all 4 angles =
`4 * 90 = 360` degrees.

Rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides the same length. The sum of all angles in rhombus is 360 degrees.

2. Parallelogram which have both pairs of opposite angles that are congruent.

Rectangle is a quadrilateral with each angle as right angle. Therefore, both pairs of opposite angles that are congruent.

Square is a quadrilateral with each angle as right angle. Therefore, both pairs of opposite angles that are congruent.

Rhombus is a quadrilateral with equal opposite sides and opposite angles. Therefore, both pairs of opposite angles that are congruent.

3. Parallelogram which have four right angles

Rectangle and Square are the parallelograms which have four right angles.