Question

Name the quadrilaterals whose diagonals are equal.
Answer: Square; rectangle

• A. True
• B. False

Answer 1

The correct option is A True

A rectangle is a quadrilateral with opposite sides equal & parallel to each other.

Each angle is a right one.

In the figure, ABCD is a rectangle whose diagonals divide it into 4 $\Delta s$ viz. $\Delta ABC$, $\Delta ADC$, $\Delta ABD$ & $\Delta CBD$

Since all the angles are right ones, the above $\Delta s$ are right $\Delta s.$

So, ${AC}^2={AB}^2+{BC}^2$ & ${BD}^2={CD}^2+{BC}^2$

But $AB=CD$ ...(opposite sides of a rectangle)

$⟹{AC}^2={BD}^2$

$⟹AC=BD.$

So, the diagonals of a rectangle are equal.

Again a square is a special rectangle whose all sides are equal to each other.

$\therefore$ The diagonals of a square are equal.