Are all acute triangles the same?

Answer 1

Mathematics is a discipline where exactitude is all-important.

Whether all acute triangles are 'the same' depends on what you mean by same. Here are some possibilities for 'same', and whether all acute triangles qualify.

• The triangles are congruent (one fits exactly on top of another) ? No.
• The triangles are similar (same three angles) ? No
• Each of the three angles is less than 900 ? Yes
• Same no of sides ? Yes
• A polygon ? Yes.
• A plane figure ? Yes.

All acute triangles meet the last four criteria; some may meet the first two as well, but not all of them.