Question

In the given figure, triangles ABC and DCB are right angled at A and D respectively and AC = DB, then $△$ABC $\cong$ $△$DCB by ________

criterion.

• A. AAA
• B. SAS
• C. ASS
• D. None of these

Answer 1

Answer: (D)

The correct option is D None of these or C. SSS

Method 1

$△ABC$ and $△DCB$ both are right angled triangle.

$\Rightarrow$ Both triangle have common hypotenuse.

$\Rightarrow$ In $△ABC$ and $△DCB$

$\Rightarrow$ $AC=DB$ [Given]

$\Rightarrow$ $BC=CB$ [Common side]

$\Rightarrow \angle BAC=\angle BDC={90}^{\circ }$

$\therefore$ $△ABC\cong △DCB$ [By $RHS$ property]

$\Rightarrow$ RHS property does not present in option

Method 2

Since, both the $△ABC$ and $△DCB$ have same common and equal side and equal hypotenuse, therefore, we can say that by Pythagoras theorem, the third corresponding side of both the triangles is also equal. Hence, we can say that,

$△ABC\cong △DCB$ by SSS congruency rule as well.