Rectangle: Property

How to use the properties of a rectangle to solve the related problems: definition, 2 properties (sides, diagonals), 2 examples, and their solutions.

Definition

Definition

A rectangle is a parallelogram
whose interior angles are all right angles: 90º.

So a rectangle
has all the properties of a parallelogram.

Property: Sides

Property

For a rectangle,
the opposite sides are congruent.

(This is also true for a parallelogram.)

Example 1

Example

Solution

If ABCD is a rectangle,
then ∠D is a right angle.

AB and DC are the opposite sides.
So AB and DC are congruent.

AB = 12

So DC = 12.

See △ADC.
It's a right triangle.

The sides are (5, 12, AC).
So this right triangle is
a (5, 12, 13) right triangle.

Pythagorean Triple

So AC = 13.

Write AC = 13.

So 13 is the answer.

Property: Diagonals

Property

For a rectangle,
the segments formed by the diagonals
are all congruent.

Example 2

Example

Solution

The given quadrilateral is a rectangle.

So the segments formed by the diagonals
are all congruent: 5.

See this right triangle.

The sides are (6, x, 5 + 5) = (6, x, 10).

(6, x, 10) looks like the multiple of (3, 4, 5).

So draw a (3, 4, 5) right triangle.

These two triangles are similar.

Then their sides are proportional.

So x/4 = 10/5.

Similar Triangles

10/5 = 2

x/4 = 2

Multiply 4 to both sides.

Then x = 8.

So x = 8.