Table of Contents

## What shapes are congruent diagonals?

Quadrilaterals

A | B |
---|---|

in these quadrilaterals, the diagonals bisect each other | paralellogram, rectangle, rhombus, square |

in these quadrilaterals, the diagonals are congruent | rectangle, square, isosceles trapezoid |

in these quadrilaterals, each of the diagonals bisects a pair of opposite angles | rhombus, square |

### What quadrilateral has congruent diagonals?

Rectangle is the quadrilateral, which has diagonals that are congruent and bisect but are not perpendicular.

#### What parallelogram has congruent diagonals?

rectangle

A parallelogram with congruent diagonals must be a rectangle. Some rhombuses are rectangles. The diagonals of a rhombus are congruent.

**Are diagonals congruent in a rectangle?**

A rectangle is a parallelogram, so its opposite sides are equal. The diagonals of a rectangle are equal and bisect each other.

**Is a square congruent?**

Square: A quadrilateral with four congruent sides and four right angles. Squares are special types of parallelograms, rectangles, and rhombuses. It has properties of all three, yet also has its own unique features. All the sides in a square are congruent.

## Are rectangles diagonals congruent?

Rectangle: A parallelogram with a right angle. When the diagonals are drawn, they bisect each other. The diagonals themselves are congruent, so each bisected line segment is also congruent. The four triangles formed from the diagonals will be congruent to the one opposite itself.

### Do rectangles have congruent diagonals?

The rectangle has the following properties: All angles are right angles by definition. The diagonals are congruent.

#### Does a rhombus have congruent diagonals?

A rhombus is a type of parallelogram, and what distinguishes its shape is that all four of its sides are congruent. All 4 sides are congruent. Diagonals bisect vertex angles. Diagonals are perpendicular.

**Does a trapezoid have congruent diagonals?**

The diagonals of an isosceles trapezoid are also congruent, but they do NOT bisect each other. Isosceles Trapezoid Diagonals Theorem: The diagonals of an isosceles trapezoid are congruent. The midsegment (of a trapezoid) is a line segment that connects the midpoints of the non-parallel sides.

**Why are the diagonals of a rectangle equal?**

Yes, the diagonals of a rectangle are equal. This is because the two diagonals are the hypotenuse of the two right angled triangles formed by the diagonals. Since, the height and base of the two triangles are equal, by Pythagoras Theorem, the hypotenuse of the triangles are also equal.

## What makes a rectangle congruent?

Opposite sides of a rectangle are the same length (congruent). The angles of a rectangle are all congruent (the same size and measure.) Remember that a 90 degree angle is called a “right angle.” So, a rectangle has four right angles. Opposite angles of a rectangle are congruent.