How do you prove a quadrilateral is a rectangle?

Answer 1

You need to prove that there are two pairs of sides with equal lengths.

Imagine a rectangle

A C

B D

Since side AB is equal in length to side CD that is one equal pair. Likewise,

AC is equal to BD and is the other equal pair. Since there are two equal

parallel pairs, the angles must all be 90 degrees by rules of geometry so

it is a rectangle.

Note: The same thing may be used to prove a square, except a square has

all sides of the same length.

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If you can prove any one of these statements, then your quadrilateral

is a rectangle:

-- Opposite sides are parallel and any one angle is a right angle.

-- Opposite sides are equal and any one angle is a right angle.

-- All four angles are right angles.

-- Adjacent angles are complementary, and one of them is a right angle.

-- Opposite sides are either equal or parallel, and area is equal to the product

of two adjacent sides.

-- Diagonals are equal.