Question

Akira gave a problem to her sister Kiara. However, Kiara got stuck. Help Kiara identify whether the triangles are congruent and choose the correct option.

• A. Yes, $△$ABC $\cong$ $△$DCE
• B. No, they are not congruent
• C. Yes, $△$DCE $\cong$ $△$BAC
• D. Yes, $△$DCE $\cong$ $△$CAB

Answer 1

The correct option is D Yes, $△$DCE $\cong$ $△$CAB

In the given figure, $MD=MC=EC=EB=AB$

$\Rightarrow$ $DC=MD+MC=CE+EB=CB$ ... ( 1 )

$\Rightarrow$ Also, $AB=EC$ ...( 2 )

$\Rightarrow$ In $△DEC$ and $△CAB$

$\Rightarrow$ $DE=CA$ [given]

$\Rightarrow$ $DC=CB$ [from ( 1 ) ]

$\Rightarrow$ $EC=AB$ [Given ]

$\therefore$ $△DEC\cong △CAB$ [By SSS criteria ]