Question

show that each angle of a rectangle is a right angle

Answer 1

To Prove :

• Each angle of a rectangle is a right angle.

Solution :

Let us recall what a Rectangle is

• A Rectangle is a Parallelogram in which one angle is a right angle.

$\begin{gathered} \rm \:D \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:C \: \: \: \: \: \: \: \: \: \\ \ \: { \boxed{ \begin{gathered} \: \: \: \: \\ \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}}} \: \rm{ \: \: \: \: \: \: \: \: \: } \\ \rm{A \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: B \: \: \: \: \: \: \: \end{gathered}$

⟶ Let ABCD be a rectangle in which ∠A = 90°

⟶ We have to Show that ∠B = ∠C = ∠D = 90°

⟶ We have, AD || BC and AB is a Transversal

⟶ ∠A + ∠B = 180°

• (interior angles on the same side of the transversal)

⟶ 90° + ∠B = 180°

⟶ ∠B = 180° - 90°

⟶ ∠B = 90°

➟ ∠C = ∠A and ∠D = ∠B

• (Opposite angles of the Parallelogram)

➟ ∠C = ∠A and ∠D = ∠B

➟ ∠C = 90° and ∠D = 90°

Therefore, each of the angles of a rectangle is a right angle.

________________

Answer 2

Question

To show that each angle of a rectangle is right angle.

Solution

Let a rectangle be ABCD

The diagonals of triangle are equal..

∴AC=BD or DB

<ABC + <DCB =180°

Adjacent angles of a parallelogram are supplementary/co-interior angles..

∴<ABC+<DCB=90°

And<ABC=<ADC=90°

And<DCB=<BAC=90°

Opposite angle of parallelogram are always equal..

Hence each angle of a rectangle is right angle