Question

Is diagonals of a rhombus bisect each other at right angles?

Answer 1

Answer:

Yes they bisect each other at 90 degree(right angles).

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Given

QWER is a rhombus

To Prove :-

AK = KE , KW = KR also QE ⊥ WR

Proof :-

QWER is a rhombus

QWER is a parallelogram such that

QW = WE = ER = RQ. ... (1)

Diagonal of ||gm bisect each other

WK = KR and QK = KE .... (2)

Now,

In ∆QKW and ∆EKW

QW = WE ... (From 1)

QK = KE ..... (From 2)

KW = KW (Common)

∆QKW ≅ ∆EKW (SAS rule)

∠QKW = ∠WKE (CPCT)

But,

∠QKW + ∠WKE = 180°

∠QKW = ∠WKE = 90°

Therefore,

QK ⊥ WK

Hence,

QE ⊥ WR and QK = KE

KW = KR