Question

$\Delta ABC$ and $\Delta ABD$ are on a common base $AB$ and $AC=BD$ and $BC=AD$ as shown in Figure. Which of the following statements is true?

• A. $\Delta ABC\cong \Delta BAD$
• B. $\Delta ABC\cong \Delta ADB$
• C. None of the above
• D. $\Delta ABC\cong \Delta ABD$

Answer 1

The correct option is A $\Delta ABC\cong \Delta BAD$

In $\Delta ABC$ and $\Delta BAD$ we have,
$AC=BD$ (given)
$BC=AD$ (given)
And $AB=BA$ (corresponding parts of congruent triangles)

Therefore, by $SSS$ criterion of congruency, $\Delta ABC\cong \Delta BAD$
Option $\text{C}$ is the correct answer.