Question

State whether the following triangles are congruent or not? Give reasons for your answer.

Answer 1

In $△FED$,

$\angle F+\angle E+\angle D={180}^{\circ }$ (Angles Sum property of a triangle)

${70}^{\circ }+\angle E+{60}^{\circ }={180}^{\circ }\angle E={50}^{\circ }$

So, In $△ABC$ and $△DEF$,

Given that:

$\angle B=\angle E$

$BC=EF$

$\angle C=\angle E$

So, $△ABC\cong △DEF$ {using $ASA$ criterion}

In $△LMN$ and $△RTS$

Given that:

$\angle M=\angle T$

$MN=ST$

$NL=SR$

So, $△LMN\cong △RTS$ {using $ASS$ criterion}