Question

In the given figure, if AB = CD and BC = DA, then which of the following is true?

• A. $△ABC\cong △CDA$ by SSS postulate
• B. $△ABC\cong △CDA$ by SSS postulate
• C. AB // CD
• D. BC // AD

Answer 1

Answer: (B), (C), (D)

The correct options are
B

$△ABC\cong △CDA$ by SSS postulate

C

AB // CD

D

BC // AD

In $△ABC$ and $△ADC$

(i) AB = CD ..... (given)

(ii) BC = DA ..... (given)

(iii) AC = AC ..... (common)

(iv) $△ABC\cong △ADC$ ..... (SSS Postulate)

(v) $\angle BAC=\angle DCA$ .....(cpct)

$\therefore$ $\text{AB}\parallel \text{CD}$ ......(alternate angles are equal)

(vi) BCA = DAC .....(cpct)

$\therefore$ $\text{BC}\parallel \text{AD}$ .....(alternate angles are equal)

Hence (B), (C) and (D)