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Which condition of congruence proves that the following pair of triangles are congruent ?
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$A.$ A.A.S
$B.$ S.S.S
$C.$ S.A.S
$D.$ A.S.A

Last updated date: 20th Jul 2024
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Hint: Here we go through by writing the conditions that are given through the diagram and after writing them we get to know that by which condition of congruence the triangles are congruent.

Complete step-by-step answer:
Here the given triangle is $\vartriangle ABC$ and $\vartriangle DEF$.
In $\vartriangle ABC$ and $\vartriangle DEF$.
Side AC=DF (Given in the figure).
Angle $\angle ACB = \angle FDE$ (Given in the figure).
Side BC=EF (Given in the figure).
And we know that if any two sides and angles included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by side angle side (SAS) rule.
Therefore $\vartriangle ABC \cong \vartriangle DEF$ According to S.A.S condition of congruence.
Hence option C is the correct answer.

Note: Whenever we face such a type of question on congruence of triangles the key concept for solving such problems is first write the condition that is given in the question and then find out which criteria of congruence is satisfying the conditions that is given in the question to find out the answer.