If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent. State whether the statement is true or false.
Solution:
Given, if the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent.
We have to determine if the given statement is true or false.
RHS congruence theorem states that, if the hypotenuse and side of one right-angled triangle are equal to the hypotenuse and the corresponding side of another right-angled triangle, the two triangles are congruent.
By RHS rule, it is clear that the hypotenuse and the corresponding side of the triangles must be equal.
According to the question,
The hypotenuse of both the triangles are equal.
RHS rule does not apply in this case.
Therefore, the given two triangles are not congruent.
✦ Try This: If the acute of one right triangle is equal to the acute of another right triangle, then the triangles are congruent. State whether the statement is true or false.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 103
If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent. State whether the statement is true or false.
Summary:
The given statement,”If the hypotenuse of one right triangle is equal to the hypotenuse of another right triangle, then the triangles are congruent” is false.
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