45°

## Do diagonals of a rhombus form right angles?

No matter what angles you have for the rhombus’s four vertices, the diagonals of a rhombus are always at right angles to each other. These diagonals also cut each other exactly in half. Geometricians say they bisect each other.

## How do you prove diagonals bisect each other in a rhombus?

Theorem: The diagonals of a parallelogram bisect each other. Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

## Where are the diagonals of a rhombus?

Diagonals of a rhombus In any rhombus, the diagonals (lines linking opposite corners) bisect each other at right angles (90°). That is, each diagonal cuts the other into two equal parts, and the angle where they cross is always 90 degrees.

## How do you prove a rhombus is a rectangle?

THEOREM Converse: If a parallelogram has congruent diagonals, it is a rectangle. the figure joining, in order, the midpoints of the sides of a rectangle is a rhombus, and the figure joining, in order, the midpoints of the sides of a rhombus is a rectangle.

## What is the theorem of rectangle?

Theorems. The isoperimetric theorem for rectangles states that among all rectangles of a given perimeter, the square has the largest area. The midpoints of the sides of any quadrilateral with perpendicular diagonals form a rectangle. A parallelogram with equal diagonals is a rectangle.

## What are the 6 properties of a rectangle?

Rectangle Properties

• A rectangle is a quadrilateral.
• The opposite sides are parallel and equal to each other.
• Each interior angle is equal to 90 degrees.
• The sum of all the interior angles is equal to 360 degrees.
• The diagonals bisect each other.
• Both the diagonals have the same length.

## What is an attribute of a rectangle?

Four sides. Opposite sides parallel. Perpendicular sides. Opposite sides have equal length. All sides have equal length.

## Why can’t a square be a rectangle?

A rectangle can be tall and thin, short and fat or all the sides can have the same length. Thus every square is a rectangle because it is a quadrilateral with all four angles right angles. However not every rectangle is a square, to be a square its sides must have the same length.