Question

Statement 1: Diagonals of a rhombus intersect at right angles.

Statement 2: All sides of a rhombus are equal.

Choose the correct statement.

• A. Statement 1 and statement 2, both are true
• B. Statement 1 and statement 2, both are false
• C. Statement 1 is true, statement 2 is false
• D. Statement 1 is false, statement 2 is true

Answer 1

The correct option is A

Statement 1 and statement 2, both are true

A rhombus is a parallelogram whose all sides are equal.

The diagonals of a rhombus intersect at right angles.
Proof-
In $△AOBand△AOD$
$AB=AD$ ( all sides are equal in rhombus )
also diagonals bisect each other
$DO=OB$
AO is common
$\therefore △$ AOD $\cong$ $△$ AOB (SSS postulate)
$\angle$ AOD = $\angle$ AOB.....c.p.c.t.
$\angle$ AOD + $\angle$ AOB =180° (Linear pair)
$2\angle$ AOD = 180°
$\Rightarrow$ $\angle$ AOD = $\angle$ AOB = ${90}^{\circ }$
The diagonals of a rhombus intersect at right angles, and all of its sides are equal.