Question

In the given figure, $BC=DC$ and $\angle ABC$ and $\angle ADC$ are right angles. Which of the following statements are correct?

• A. $\Delta ABC\cong \Delta ADC$ by SAS postulate
• B. $\Delta ABC\cong \Delta ADC$ by ASA postulate
• C. $\Delta ABC\cong \Delta ADC$ by RHS postulate
• D. AC bisects $\angle BAD$

Answer 1

Answer: (C), (D)

The correct options are
C

$\Delta ABC\cong \Delta ADC$ by RHS postulate

D

AC bisects $\angle BAD$

In $\Delta ABC$ and $\Delta ADC$

(i) $\angle ABC=\angle ADC={90}^{\circ }$ ……….(given)

(ii) $AC=AC$ ………(common)

(iii) $BC=DC$ ………(given)

(iv) $\Delta ABC\cong \Delta ACD$ …… (RHS postulate)

(v) $\angle BAC=\angle DAC$ ……..(cpct)

(vi) therefore AC bisects $\angle BAD$ ….. (from (v) )

Ans: Hence (C) and (D)