Question

In the given figure, BD bisects $\angle ABC$ and BD is perpendicular to AC. Which of the following statements are correct?

• A. $\Delta ABD\cong \Delta CBD$ by ASA postulate
• B. $\Delta ABD\cong \Delta CBD$ by RHS postulate
• C. BD bisects AC
• D. $BA=BC$

Answer 1

Answer: (A), (C), (D)

The correct options are
A

$\Delta ABD\cong \Delta CBD$ by ASA postulate

C

BD bisects AC

D

$BA=BC$

In $\Delta ABD$ and $\Delta CBD$

(i) $\angle ABD=\angle CBD$ ……. (given )

(ii) $BD=BD$ ………(common)

(iii) $\angle BDA=\angle BDC={90}^{\circ }$ ……….(given)

(iv) $\Delta ABD\cong \Delta CBD$ …… (ASA postulate)

(v) $BA=BC$ ……..(cpct)

(vi) $AD=DC$ ……..(cpct)

(vii) BD bisects AC …… (from (vi) )

Ans: Hence (A), (C) and (D)