$△ F G C$ is an isosceles triangle, which of the following method will prove $△ A B C$ congruent to $△ D E F$ ?

SSS

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RHS

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AAS

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SAS

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Solution

The correct option is D RHS
In $△ A B C$ and $△ D E F$

Given,
$A B = D E$
$∠ A B C = ∠ D E F = 90^{\circ}$

$△ F C G$ is isoceles, $G F = G C$ $⟹ F D = C A$ ...... (as $A B | | D E$ , $G D$ should be equal to $G A$ )

$A C = F D$

Hence, $△ A B C ≅ △ D E F$ by $R H S p o s t u l a t e$

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△FGC is an isosceles triangle, which of the following method will prove △ABC congruent to △DEF ?

The correct option is D RHSIn △ABC and △DEFGiven,AB=DE∠ABC=∠DEF=90∘△FCG is isoceles, GF=GC ⟹FD=CA ...... (as AB||DE, GD should be equal to GA)AC=FDHence, △ABC≅△DEF by RHS postulate

$△ F G C$ is an isosceles triangle, which of the following method will prove $△ A B C$ congruent to $△ D E F$ ?