Question

Prove that the diagonals of a rectangle are equal in length

Answer 1

Consider triangle ABCD
ABCD is a rectangle. AC and BD are the diagonals of rectangle.

In ΔABC and ΔBCD, we have

AB = CD (Opposite sides of rectangle are equal)

∠ABC = ∠BCD  ( Each equal to 90°)

BC = BC (Common)

∴ ΔABC ΔBCD (SAS congruence criterion)

⇒ AC = BD [c.p.c.t]

Hence, the diagonals of a rectangle are equal.

Answer 2

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

Given

QWER is a rectangle whose diagonal are QE and WR

To Prove,

QE = WR

Proof :-

Since the QWER is a rectangle

QWER is a parallelogram and it's one angle is right angle.

Assume,

∠W = 90°

Now,

∠E + ∠E = 180°

Therefore,

∠E = ∠E = 90°

Now,

In ∆QWE and ∆REW

WE = WE (Common)

∠E = ∠E (Each angle 90°)

QW = RE

Therefore,

∆QWE ≅ ∆REW (SAS rule)

So,

QE = WR (CPCT)