Question

Match the figures in Column-I with their corresponding congruence criterion given in Column-II.

• A. (i) $\to$ (b), (ii) $\to$ (d), (iii) $\to$ (a), (iv) $\to$ (c)
• B. (i) $\to$ (c), (ii) $\to$ (a), (iii) $\to$ (b), (iv) $\to$ (d)
• C. (i) $\to$ (b), (ii) $\to$ (c), (iii) $\to$ (a), (iv) $\to$ (d)
• D. (i) $\to$ (a), (ii) $\to$ (c), (iii) $\to$ (b), (iv) $\to$ (d)

Answer 1

Answer: (C)

(i) $\to$ (b), (ii) $\to$ (c), (iii) $\to$ (a), (iv) $\to$ (d)

In fig (i), $△ADB$ and $△ADC$

It is given that, $AB=AC$, $\angle ADB=\angle ADC={90}^o$ and $AD=AD$

$\therefore$ So, By RHS criteria $$△ADB\cong △ADC$

In fig (ii), $△BAD$ and $△DCB$

It is given that, $BA=DC,AD=CB$ and $BD=DB$

$\therefore$ By SSS criteria $△BAD\cong △DCB$

In fig (iii), $△ABC$ and $△CDA$

$AB\parallel CD$ and $BC\parallel DA$

$\angle BAC=\angle DCA$ and $\angle BCA=\angle DAC$ [Alternate angles between parallel lines]

$AC=CA$ [Common side]

$\therefore$ $△ABC\cong △CDA$, by ASA criteria.

In fig (iv), $△ABE$ and $△DCE$

It is given that, $AB=DC,\angle A=\angle D$ and $AE=DE$

$\therefore$ $△ABE\cong △DCE$, by SAS criteria.

$\therefore$ Correct answer is option $C.$