Question

Complete each statement with the word always, sometimes, or never.

An obtuse triangle is $\underset{¯}{?}$a right triangle.

Short answer

An obtuse triangle is never a right triangle.

Step-by-step solution

Step 1. Definition of an obtuse triangle.

An obtuse triangle is one that has one of the angles measure greater than $\mathbf{90}\mathbf{°}$.

Step 2. Description of step.

The sum of all the three angles in a triangle is $90°$.

An obtuse triangle is one that has one of the angles measure greater than $90°$.

Therefore, for the obtuse triangle, the sum of the other two angles should be less than $90°$.

Therefore, in the obtuse triangle, no angle can be equal to $90°$.

Step 3. Write the conclusion.

Therefore, in the obtuse triangle, no angle can be a right angle.

Therefore, an obtuse triangle is never a right triangle.