Triangle

Equilateral Triangle

The equilateral triangle has all three sides that are equal length, and consequently all three interior angles are equal size also.  And because of that, those angles all equal 60°.  The problem sometimes tells you that a triangle is an equilateral triangle, sometimes, it may use tic marks through the triangle sides to indicate the sides that are the same length.

Isosceles Triangle

Unlike the equilateral triangle, the isosceles triangle has only two sides that are the same length and the other side a different length. Again, the problem may state which sides are equal, or tic marks may tell you.  The angles that are opposite the equal sides are also equal.

There is a special isosceles triangle called the 45°-45°-90°triangle.  We’ll talk about it’s properties when we talk more about trig.

Scalene Triangle

The scalene triangle is one that has no sides that are of equal length.  That also means that none of the interior angles are equal in size either.  Be careful not to make assumptions about the triangle that you aren’t told in the problem.  If none of the sides are equal, then even if it looks like it, none of the angles are equal either.

Right Triangle

The right triangle has exactly ONE angle that is 90°.  It has some special properties, like the Pythagorean Theorem.  You can also use trig functions to calculate length of sides.

The problem will tell you that the triangle is a right triangle, or there will be a little box (as seen below) in the angle that is the right angle.

There are always questions that deal with right triangles on the ACT Math test.

Obtuse Triangle

An obtuse triangle is a triangle where one (and only one) angle is an obtuse angle (it’s greater than 90°).

Acute Triangle

Finally, an acute triangle is a triangle where all of the angles are acute angles.