Question

what can you say about the quadrilateral ABCD given in figure 10.22? Is it a rectangle? justify your answer.​​

Answer 1

Answer:

Hola mate

Step-by-step explanation:

QUADRILATERAL ABCD IS EITHER A RECTANGLE OR A SQUARE.

But, since a square is also a rectangle. Hence, ABCD is a rectangle.

JUSTIFICATION :-

(please refer to the above photograph for the angle names)

Now,

Given that :- Angle 1 = angle 3 = 90 degrees

Now,

Angle 1 + angle 2 = 180 (linear pair)

So,

Angle 2 = 180 - 90 = 90 degrees.

So,

Angle 2 = 90 = angle 3.

Thus

In quadrilateral ABCD, we find that opposite angles are equal (angle 2 = angle 3)

So,

ABCD is a parallelogram.

So,

This implies that :-

'l' ll 'm' and 'p' ll 'q'

So,

Angle 2 + Angle 4 = 180

(Sum of Co-interior Angles)

Thus,

Angle 4 = 180 - 90 = 90

Also,

Angle 4 = angle 5

(opposite angles of parallelogram are equal)

So, Angle 5 = 90 degrees

Now,

In quadrilateral ABCD :-

Angle 1 = 90

Angle 2 =90

Angle 3 =90

Angle 4 =90

So ,

If all angles of a quadrilateral is equal to 90 degrees, the quadrilateral will be either rectangle or square.

But , here nothing is given that

AB = BC = CD =DA

So, ABCD is a rectangle.

Hence, justified.

Thanks!

Aim of thanks 40

Answer 2

From the fig,l ∥ m

∴AB∥CD

∠ADC+∠EDC=180° −−−(linear pair)

⇒∠ADC=180°−90°⇒∠ADC=90°and ∠EDC=∠DAB=90° −−−(corresponding angles)

Also, ∠FCD=∠ABC=90° −−−(corresponding angles)

∴∠DCB+∠FCD=180° −−−(linear pair)

⇒∠DCB+90°=180°

⇒∠DCB=90°

In quad ABCD

∵ AB∥CD, AB=CD and BC∥AD, BC=AD

also sum of angles on same side of transversal is 180° (∠DCB+∠ABC=90°+90°=180°)

∴ ABCD is a parallelogram.Also, measure of each angle is 90° and opp. sides are parallel and equal.

∴ABCD is a rectangle.