CBSE Class 9 Answered

Construction : Produce AB and draw a line CE || AD.

Proof :

(i) Since AD || CE and transversal AE cuts them at A and E respectively.

A + E = 180° ...(1)

Since AB || CD and AD || CE, AECD is a parallelogram.

AD = CE

BC = CE (AD = BC (given))

Thus, In BCE, we have

BC = CE

CBE = CEB

180° -B = E

B + E = 180° ...(2)

from (1) and (2), we get,

A + E = B + E

A = B

(ii) Since A = B

BAD = ABD

180° - BAD = 180° - ABD

ADB = BCD

D = C

i.e. C = D

(iii) In ABC and BAD,

we have BC = AD (given)

AB = AB (common)

A = B (proved above)

(SAS Congruence condition)