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Figure 1 The relationship of the square of the longest side to the sum of the squares of the other two sides of a right triangle, an obtuse triangle, and an acute triangle.

Example 1: Determine whether the following sets of three values could be the lengths of the sides of a triangle. If the values can be the sides of a triangle, then classify the triangle. (a) 16‐30‐34, (b) 5‐5‐8, (c) 5‐8‐15, (d) 4‐4‐5, (e) 9‐12‐16, (f) (Recall the Triangle Inequality Theorem, Theorem 38, which states that the longest side in any triangle must be less than the sum of the two shorter sides.)a. This is a right triangle. Because its sides are of different lengths, it is also a scalene triangle.b.

This is an obtuse triangle. Because two of its sides are of equal measure, it is also an isosceles triangle.

c.

d.

This is an acute triangle. Because two of its sides are of equal measure, it is also an isosceles triangle.

e.

This is an obtuse triangle. Because all sides are of different lengths, it is also a scalene triangle.

f.

This is a right triangle. Because two of its sides are of equal measure, it is also an isosceles triangle.