Question

In Fig. 6.53, ∠1 = ∠ 2 and ∠ 3 = ∠ 4. 

(i) Is ΔADC ≅ ΔABC? Why ? 

(ii) Show that AD = AB and CD = CB.

Answer 1

(i) The correct answer is yes, (ASA)

(ii) AD = DB & CD = CB (By CPCT)

Explanation:

In ΔADC &  ΔABC,
∠1 = ∠ 2 ....... (Given)
AC = AC ..........(Common)
∠ 3 = ∠ 4 .......(Given)

Thus,

ΔADC ≅ ΔABC (By ASA)

Hence, AD = AB (By CPCT)
CD = DB (Also by CPCT)

*CPCT = Corresponding parts of congruent triangles are equal.