Properties of Quadrilaterals and Their Diagonals

This lesson covers the properties of special parallelograms: rhombuses, rectangles, and squares. A rhombus is a parallelogram with four congruent sides, and its diagonals are perpendicular and bisect the angles. A rectangle is a parallelogram with four right angles, and its diagonals are congruent. A square combines the properties of both a rhombus and a rectangle, having four congruent sides and four right angles. The lesson emphasizes the unique properties of each shape while reinforcing their shared characteristics as parallelograms.

What is a special characteristic of a rhombus?

• It has four right angles.

• It has no parallel sides.

• It has four congruent sides.

• Its diagonals are congruent.

What is the relationship between the sides of a rhombus?

• Opposite sides are congruent.

• Adjacent sides are perpendicular.

• All sides are congruent.

• All sides are parallel.

What is a defining characteristic of a rhombus?

• It has no parallel sides.

• Its diagonals are congruent.

• It has four congruent sides.

• It has four right angles.

Which of the following is true about a rectangle?

• It has no parallel sides.

• Its diagonals are perpendicular.

• It has four congruent sides.

• It has four right angles.

Which of the following is NOT a property of a rectangle?

• Opposite sides are parallel

• Congruent diagonals

• Four congruent sides

• Four right angles

What is true about the angles in a rectangle?

• All angles are acute.

• All angles are obtuse.

• All angles are right angles.

• Angles are not congruent.

How can a square be described in terms of other shapes?

• As a combination of a rhombus and a rectangle.

• As a combination of two triangles.

• As a combination of a circle and a rectangle.

• As a combination of two rectangles.

What is a defining feature of a square?

• Its diagonals are not congruent.

• It has no right angles.

• It has four congruent sides and four right angles.

• It has only one pair of parallel sides.

Which property is common to all parallelograms?

• Opposite sides are parallel.

• Diagonals are perpendicular.

• All sides are congruent.

• All angles are right angles.

What is a common property of the diagonals in all parallelograms?

• They are perpendicular.

• They bisect each other.

• They are congruent.

• They do not intersect.