Question

class 9th ncert maths book ​

Answer 1

Answer:

Yes this is maths ncert book because I have also this book

Answer 2

i. DC is equal to AB is equal to AD is equal to BC.

ii. ∠CBD is equal to ABC and ∠ADC is equal to ∠CDB

Given:

AB= DC

BC=AD

AC= Diagonal

∠BAC= ∠DAC

∠ACB= ∠ACD

To prove:

i. ABCD is a square.

ii. BD bisects ∠B and ∠D.

Proof:

Join the diagonal BD and let the diagonals meet each other at a point M.

i. In ΔAMB and ΔAMD

AM=AM  (Common side)

∠AMD= ∠AMB= 90°  (Diagonals of a rectangle bisect each other at 90°)

DM= BM ( Diagonals of a rectangle bisect each other)

∴ ΔAMB ≅ ΔAMD by SAS criteria.

Since, ΔAMB ≅ ΔAMD so AD= AB.

But, BC=AD and AB= DC.

Thus, we can say that DC=AB=AD=BC.

Since,  DC=AB=AD=BC.

Therefore, ABCD is a square.

ii. In ΔBAD and ΔBCD

BC= AD (Given)

AB= DC (Given)

∠BCD= ∠BAD= 90° (Each angle of a rectangle is 90°)

∴ ΔBAD ≅ ΔBCD by SAS criteria.

Since, ΔBAD ≅ ΔBCD so ∠CBD= ABC and ∠ADC= ∠CDB.

Therefore, BD bisects ∠B and ∠D.

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