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Standard IX

Mathematics

SSS Criteria for Congruency

AC is a diago...

Question

AC is a diagonal of a rectangle ABCD. Which triangle is congruent to $△$ ADC?

△ B C A

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△ A C B

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△ C B A

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△ B C D

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Solution

The correct option is C $△ C B A$

In $△ A D C$ and $△ C B A$ ,

$A D = C B$ (Opposite sides of rectangle)

$D C = B A$ (Opposite sides of the rectangle)

$A C = C A$ (Common side)

$△ A D C ≅ △ C B A$ by $S S S$ criteria.

So option $C$ is correct.

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Suppose ABCD is rectangle. Using RHS theorem, prove that triangles ABC and ADC are congruent.

$A B C D$ is a trapezium in which $A B ∥ C D$ and $A D = B C$ show that
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IV) diagonal $A C$ =diagonal $B D$

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AC is a diagonal of a rectangle ABCD. Which triangle is congruent to △ ADC?

The correct option is C △CBAIn △ADC and △CBA,AD=CB (Opposite sides of rectangle)DC=BA (Opposite sides of the rectangle)AC=CA (Common side)△ADC≅△CBA by SSS criteria.So option C is correct.

AC is a diagonal of a rectangle ABCD. Which triangle is congruent to $△$ ADC?

The correct option is C $△ C B A$

In $△ A D C$ and $△ C B A$ ,

$A D = C B$ (Opposite sides of rectangle)

$D C = B A$ (Opposite sides of the rectangle)

$A C = C A$ (Common side)

$△ A D C ≅ △ C B A$ by $S S S$ criteria.

So option $C$ is correct.