RIANGLESABCD is a quadrilateral in which AD =BC andDAB CBA (see Fig.7.

1.	RIANGLESABCD is a quadrilateral in which AD =BC andDAB CBA (see Fig.7.17) Prove that(i)ΔΑΒΙ)(ii) BD#ACABD-ABAC(iii)BAC.Fig.737diculars to a line
Answer» Given: In quadrilateral ABCD,AD = BC & ∠DAB = ∠CBA To Prove: (i)ΔABD ≅ ΔBAC (ii)BD=AC (iii)∠ABD = ∠BAC Proof: i)In ΔABD & ΔBAC, AB = BA (Common)∠DAB = ∠CBA (Given)AD = BC (Given) Hence,ΔABD ≅ΔBAC. ( by SAS congruence rule).(ii) Since, ΔABD ≅ΔBACThen, BD = AC (by CPCT) (iii)Since, ΔABD ≅ ΔBAC Then , ∠ABD = ∠BAC (by CPCT) hit like if you find it useful

RIANGLESABCD is a quadrilateral in which AD =BC andDAB CBA (see Fig.7.17) Prove that(i)ΔΑΒΙ)(ii) BD#ACABD-ABAC(iii)BAC.Fig.737diculars to a line

Answer»

Given:

In quadrilateral ABCD,AD = BC & ∠DAB = ∠CBA

To Prove:

(i)ΔABD ≅ ΔBAC

(ii)BD=AC

(iii)∠ABD = ∠BAC

Proof:

i)In ΔABD & ΔBAC,

AB = BA (Common)∠DAB = ∠CBA (Given)AD = BC (Given)

Hence,ΔABD ≅ΔBAC.

( by SAS congruence rule).(ii) Since, ΔABD ≅ΔBACThen, BD = AC (by CPCT)

(iii)Since, ΔABD ≅ ΔBAC

Then , ∠ABD = ∠BAC (by CPCT)

hit like if you find it useful