Diagonal AC of อ paiallelapin ABCD hintaA ee ig 819) Show that6.ABCD

1.	Diagonal AC of อ paiallelapin ABCD hintaA ee ig 819) Show that6.ABCD is a rhombus
Answer» i)In ΔADC and ΔCBA, AD = CB (Opposite sides of a \|\|gm) DC = BA (Opposite sides of a \|\|gm) AC = CA (Common) Therefore, ΔADC ≅ ΔCBA ( by SSS congruence rule.) ∠ACD = ∠CAB ……(i) (by CPCT) ∠BCA= ∠CAD…..(ii) (By CPCT) & ∠CAB = ∠CAD…..(iii) (Given) From eq i,ii,iii, All 4 above angles are equal to each other.. Hence, ∠ACD = ∠BCA Thus, AC bisects ∠C also. (ii) ∠ACD = ∠CAD (Proved) AD = CD (Opposite sides of equal anglesof a triangle are equal) But, AB= CD & AD= BC [Opposite sides of a parallelogram] AB = BC = CD = DA Hence, ABCD is a rhombus.

Diagonal AC of อ paiallelapin ABCD hintaA ee ig 819) Show that6.ABCD is a rhombus

Answer»

i)In ΔADC and ΔCBA,

AD = CB

(Opposite sides of a ||gm)

DC = BA

(Opposite sides of a ||gm)

AC = CA (Common)

Therefore,

ΔADC ≅ ΔCBA

( by SSS congruence rule.)

∠ACD = ∠CAB ……(i)

(by CPCT)

∠BCA= ∠CAD…..(ii)

(By CPCT)

& ∠CAB = ∠CAD…..(iii)

(Given)

From eq i,ii,iii,

All 4 above angles are equal to each other..

Hence, ∠ACD = ∠BCA

Thus, AC bisects ∠C also.

(ii) ∠ACD = ∠CAD (Proved)

AD = CD (Opposite sides of equal anglesof a triangle are equal)

But, AB= CD & AD= BC

[Opposite sides of a parallelogram]

AB = BC = CD = DA

Hence, ABCD is a rhombus.