A congruence theorem for two right angled triangles

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Question from Sayari, a student:

Hello.
Is it possible for two right angled triangles to have the same length of base and height and a different hypotenuse? If not so, then why in the congruence criteria RHS the hypotenuse is given more importance? It can also be like- 'two triangles are congruent if they are right angled and have the same base and height.'
Thank You.

Hi,

Your theorem is true. If the base and height of two sides of a right triangle are equal then the angles between the two sides are right angles and you have the situation I learned as "two sides and a contained angle" or you might call SAS.

I hope this helps,
Penny

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