Question

Select the appropriate option for the given figure, if $AD\text{and}BC$ are both perpendicular to $AB$, and $BD\text{and}AC$ are equal in length.

• A. $△ABC\cong △ABD$
• B. $△ABC\cong △BAD$
• C. $△ABC\cong △BDA$
• D. $\text{Triangles not congruent}$

Answer 1

The correct option is B $△ABC\cong △BAD$


In the $△ABC\text{and}△BAD,$
$AC=BD$ [Given]
$\angle ABC=\angle BAD={90}^{\circ }$ [Given]
$AB=BA$ [Common]
$⟹$ $A\leftrightarrow B,B\leftrightarrow A,C\leftrightarrow D$
hence, $△ABC\cong △BAD$
[By hypotenuse leg congruency rule]