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If you name them by sidesScaleneA triangle with no congruent sides.

All sides must be different.

IsoscelesA triangle with two sides the same.

Must have one and only one different from the two that are the same.

EquilateralAll sides are congruent.

No sides may be different.

Triangle is also equiangular.

If you name by angles. All angles must add up to be 180o.Acute
  1. All angles are acute.
  2. Acute is from 1o-89o.
  3. As a subcategory, triangle may be equiangular.
  • All angles are congruent.
  • The only time that this is so is if all angles are 60o as the angles MUST add up to be 180o.
  • Triangle is also equilateral.
ObtuseOne angle is obtuse.

Obtuse is from 91o-179o, but due to angles needing to be 180o in sum, the maximum degree you can see for an angle in a triangle is 178o, and the other two being 1o.

If more than one angle is obtuse, it cannot be a triangle, as it must add up to be 180o. Just two obtuse-angles (91,91) would already add up to be 182o. And there's still a third side!

The other two angles are acute.

RightOne angle is right.

A right-angle is 90o, and due to the angles needing to be 180o in sum, there can only be one right-angle. If there were two, the sum would be 180o, but theres still one more angle.

A right-triangle has one right-angle and two acute-angles.

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