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RHS Criteria for Congruency

In two right ...

Question

In two right triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

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Solution

It is given that

We are asked to show that

Let us assume

, and are right angled triangle.

Thus in and, we have

And (given)

Hence by AAs congruence criterion we haveProved.

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In two right triangles, one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.

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Q. Which of the following statements are true and which of them are false?

(i) All squares are congruent.
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(iv) If two triangles are equal in area, they are congruent.
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(vi) If two angles and any side of a triangle are equal to the corresponding angles and the side of another triangle then the triangles are congruent.
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