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
A rectangle is a parallelogram
whose interior angles are all right angles: 90º.
So a rectangle
has all the properties of a parallelogram.
PropertySides
For a rectangle,
the opposite sides are congruent.
(This is also true for a parallelogram.)
Example
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.
PropertyDiagonals
For a rectangle,
the segments formed by the diagonals
are all congruent.
Example
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.