Question

Which of the following statements is/are false?
A) Two triangles having the same area are congruent.
B) If two sides and one angle of a triangle are equal to the corresponding two sides and the angle of another triangle, then the two triangles are congruent.
C) If the hypotenuse of one right triangle is equal to the hypotenuse of another triangle, then the triangles are congruent.
D) All of the above.

Answer 1

Hint: For solving this problem, we consider all the options individually and then analyse each option for its truth value as multiple answers are possible. We use the concept of congruence of triangles for analysing each option. By doing so, we get the final result.

Complete step-by-step answer:
Considering option (A), two triangles having the same area. The above statement is false because for triangles to be congruent corresponding sides must be equal not the area. The converse of this statement is true that if triangles are congruent then the area is the same.
Considering option (B), two sides and one angle of a triangle are equal to the corresponding two sides and the angle of another triangle, then the two triangles are congruent. It is also false because triangles are congruent if the two sides and the included angle between the sides are equal, not all the angles.
Considering option (C), the hypotenuse of one right triangle is equal to the hypotenuse of another triangle, then the triangles are congruent. It is false because for RHS congruence, one of the corresponding sides of two right triangles must be equal.
Therefore, all the options are false.
Hence, option (D) is correct.

Note: The knowledge of all the congruence rules and properties associated with triangles is required for solving this problem. This knowledge is very useful in solving various complex problems related to triangles.