Question : In $\triangle$ABC and $\triangle$DEF, $\angle$A = $55^{\circ}$, AB = DE, AC = DF, $\angle$E = $85^{\circ}$ and $\angle$F = $40^{\circ}$. By which property are $\triangle$ABC and $\triangle$DEF congruent?
Option 1: SAS property
Option 2: ASA property
Option 3: RHS property
Option 4: SSS property
Correct Answer: SAS property
Solution :
In $\triangle$ DEF,
$\angle$ D + $\angle$ E + $\angle$ F = $180^{\circ}$
⇒ $\angle$ D + $85^{\circ}$ + $40^{\circ}$ = $180^{\circ}$
⇒ $\angle$ D = $180^{\circ} - 85^{\circ} - 40^{\circ}$ = $55^{\circ}$
In $\triangle$ ABC and $\triangle$ DEF,
AB = DE
AC = DF
$\angle$ A = $\angle$ D = $55^{\circ}$
By the SAS property, $\triangle$ABC and $\triangle$DEF are congruent.
Hence, the correct answer is SAS property.
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