Question

In the given figure, AC = AD and BC = BD. Which of the following statements are correct?

• A. $\Delta ABC\cong \Delta ABD$ by SSS postulate
• B. $\Delta ABC\cong \Delta ABD$ by SAS postulate
• C. $\angle ACB=\angle ADB$
• D. AB bisects $\angle CAD$

Answer 1

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

The correct options are
A

$\Delta ABC\cong \Delta ABD$ by SSS postulate

C

$\angle ACB=\angle ADB$

D

AB bisects $\angle CAD$

In $\Delta ABC$ and $\Delta ABD$

(i) AC = AD ……………….(given)

(ii) BC = BD ……………( given)

(iii) AB = AB ………(common)

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

(v) $\angle ACB=\angle ADB$ ……..(cpct)

(vi) $\angle BAC=\angle BAD$ ……..(cpct)

(vii) therefore AB bisects $\angle CAD$ ….. (from (vi) )

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