Discussion
Which one of the following is not true ?
Answer: C
The statement that is not true is Two congruent triangles are always similar and converse is also true.
The first half is correct: congruent triangles have the same shape and size, so they are also similar. The converse fails: similar triangles have the same shape but can differ in size, for example a triangle with sides 3, 4, 5 and another with sides 6, 8, 10. So similar triangles need not be congruent.
The other statements hold. Congruent triangles have equal area. Triangles of equal area need not be congruent (a 2 by 6 right triangle and a 3 by 4 right triangle both have area 6). And triangles on equal bases can be drawn with equal perpendicular heights, which gives them equal areas.
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