# What are the theorems of a rectangle?

## What are the theorems of a 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 two theorems on rectangle?

Definition and Theorems pertaining to a rectangle: DEFINITION: A rectangle is a parallelogram with four right angles. THEOREM: If a parallelogram is a rectangle, it has congruent diagonals. THEOREM Converse: If a parallelogram has congruent diagonals, it is a rectangle.

### What are the theorems of a square?

Square and its Theorems

Statements Reasons
1) ABCD is a square. 1) Given
2) AD = BC 2) Properties of square.
3) ∠BAD = ∠ABC 3) Each 900 and by properties of square.
4) AB = BA 4) Reflexive (common side)

What are the theorems on square?

A square is a parallelogram with four congruent sides and four right angles. This definition may also be stated as A quadrilateral is a square if and only if it is a rhombus and a rectangle. Proof of Theorem: If a parallelogram is a rhombus, then the diagonals are perpendicular.

## What are the 11 properties of rectangle?

The fundamental properties of rectangles are:

• 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.

How do you prove a rectangle?

There are several easy ways to prove it is a rectangle.

1. Show that all angles are 90 degrees.
2. Show that one set of sides is parallel ,and that two opposite angles are 90 degrees.
3. Show that the diagonals bisect each other, and that they are equal in length.

Euler’s quadrilateral theorem or Euler’s law on quadrilaterals, named after Leonhard Euler (1707–1783), describes a relation between the sides of a convex quadrilateral and its diagonals. It is a generalisation of the parallelogram law which in turn can be seen as generalisation of the Pythagorean theorem.

What are the properties of all rectangles?

A rectangle is a quadrilateral with four right angles. Thus, all the angles in a rectangle are equal (360°/4 = 90°). Moreover, the opposite sides of a rectangle are parallel and equal, and diagonals bisect each other.

## What is the formula for solving the area of a rectangle?

Area of Rectangle Formula

The formula for the Area of a Rectangle
Area of a Rectangle A = l × b

How do u calculate area of a rectangle?

To find the area of a rectangle, multiply its width by its height. If we know two sides of the rectangle that are different lengths, then we have both the height and the width.

### How do you prove all the theorems?

Summary — how to prove a theorem Identify the assumptions and goals of the theorem. Understand the implications of each of the assumptions made. Translate them into mathematical definitions if you can. Make an assumption about what you are trying to prove and show that it leads to a proof or a contradiction.