Diagonal Property Of Rectangle

Theorem: Both the diagonals of a rectangle are of equal length.

Prerequisites:
Rectangle (definition)
Properties of parallelogram (proof)
SAS congruence (proof)

Proof:

Let ABCD be a rectangle having diagonals AC and BD, which intersect at a point E.

Now in $\triangle ADC$ and $\triangle BCD$,

$\qquad\quad AD = BC\qquad\qquad\qquad\qquad\qquad\text{(opposite sides of parallelogram are equal)}\\ \qquad\quad DC = DC\qquad\qquad\qquad\qquad\qquad\text{(common)}\\ \qquad\quad\angle ADC = \angle BCD = 90^o\qquad\qquad\:\text{(by definition of rectangle)}$

Hence, $\triangle ADC\cong\triangle BCD$ by SAS rule.

Therefore, by CPCTC, AC $=$ BD.

Q.E.D.


Recommended:
Characteristics of parallelogram
Angle sum property of polygon
Area of rectangle