Question

In the given figure, if AB//DC and AD // BC, then which of the following is true ?

• A. $△ABC\cong △CBD$ by RHS postulate
• B. $△ABC\cong △CDA$ by ASA postulate
• C. If $\angle ABC={75}^{\circ }$, then $\angle$ CDA = 105${}^{\circ }$
• D. If $\angle ABC={75}^{\circ }$, then $\angle$CDA = 75${}^{\circ }$

Answer 1

Answer: (B), (D)

The correct options are
B

$△ABC\cong △CDA$ by ASA postulate

D

If $\angle ABC={75}^{\circ }$, then $\angle$CDA = 75${}^{\circ }$

In $△ABC$ and $△$ CDA,

(i) $\angle$ BAC = $\angle$ DCA ....(alternate angles)

(ii) AC = AC .......(common)

(iii) $\angle BCA=\angle DAC$ .....(alternate angles )

(iv) $△ABC\cong △CDA$ .....(ASA Postulate)

(v) $\angle ABC$ = $\angle CDA$ .......(cpct)

$\therefore$ if $\angle$ ABC = 75${}^{\circ }$, then $\angle$ CDA = 75${}^{\circ }$

Hence (B), and (D)