Question

Which of the following pairs of triangles are congruent?

• A. $△ABC$ and $△DEF$ in which : $BC=EF$, $AC=DF$ and $\angle C=\angle F$
• B. $△ABC$ and $△DEF$ in which : $AB=PQ$, $BC=QR$ and $\angle C=\angle R$
• C. $△ABC$ and $△LMN$ in which : $\angle A=\angle L={90}^0$, $AB=LM$, $\angle C={40}^0$ and $\angle M={50}^0$
• D. $△ABC$ and $△DEF$ in which : and $\angle B=\angle E={50}^0$ and $AC=DF$

Answer 1

Answer: (A), (C)

The correct options are
A $△ABC$ and $△DEF$ in which : $BC=EF$, $AC=DF$ and $\angle C=\angle F$
C $△ABC$ and $△LMN$ in which : $\angle A=\angle L={90}^0$, $AB=LM$, $\angle C={40}^0$ and $\angle M={50}^0$

From Option A,
Given: $△ABC$ and $△DEF$
$BC=EF$
$AC=DF$
$\angle C=\angle F$
Thus, $△ABC\cong △DEF$ (SAS rule)
From Option C,
In $△ABC$,
Sum of angles = 180
$\angle A+\angle B+\angle C=180$
$90+\angle B+40=180$
$\angle B={50}^{\circ }$
Given, $△ABC$ and $△LMN$,
$\angle A=\angle L={90}^{\circ }$
$AB=LM$
$\angle B=\angle M={50}^{\circ }$
Thus, $△ABC\cong △LMN$ (ASA rule)