Question

11 tell which quadrilateral(s) have the given property.
a) diagonals bisect each other
b) diagonals are perpendicular
c) all sides are congruent

Explanation:

Part (a)

Step1: Recall Parallelogram Definition

A parallelogram is a quadrilateral with both pairs of opposite sides parallel.

Step2: Diagonal Property of Parallelogram

By the properties of parallelograms, in a parallelogram, the diagonals bisect each other. Rectangles, rhombuses, and squares are special types of parallelograms, so they also have this property. Non - parallelogram quadrilaterals like trapezoids (non - isosceles), kites (in a non - parallelogram way) and general quadrilaterals do not have diagonals that bisect each other.

Part (b)

Step1: Recall Rhombus Property

A rhombus is a parallelogram with all sides equal. The diagonals of a rhombus are perpendicular to each other.

Step2: Square as Special Rhombus

A square is a special type of rhombus (and also a rectangle), so its diagonals are also perpendicular.

Step3: Kite Property

A kite is a quadrilateral with two distinct pairs of adjacent sides equal. The diagonals of a kite are perpendicular to each other. Rectangles (non - square) and general parallelograms do not have perpendicular diagonals.

Part (c)

Step1: Recall Rhombus Definition

A rhombus is defined as a quadrilateral with all four sides congruent.

Step2: Square as Special Rhombus

A square is a special case of a rhombus where all angles are right angles, so it also has all sides congruent. Rectangles have opposite sides congruent, not all sides. Trapezoids and kites do not have all sides congruent.

Answer:

Parallelograms (including Rectangle, Rhombus, Square)