A square is divided into two parts by one of its diagonal. The two triangles formed are _____.

congruent

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not congruent

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obtuse angled

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insufficient data

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Solution

The correct option is A congruent

When a square ABCD is divided by its diagonals, $△ A D C$ and $△ A B C$ are formed.

In $△$ ADC and $△$ ABC
CA = CA .... (Common side)
AD = AB .... (Sides of the square)
DC = BC ..... (Sides of the square)
$∴ △ A D C ≅ △ A B C$
by SSS criterion for congruency of triangles.

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