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At a Glance - Classifying Triangles Based on Angles

Studying triangles is exactly what it sounds like—studying three angles. If that's the case, we'd better go back (to the future?) and dust some cobwebs off those angle concepts we learned a few chapters ago. Here's a quick refresher:

• Acute angles have measures of less than 90°. They're the cute little ones.
• Obtuse angles are big boys over 90°.
• Right angles aren't over or under, but exactly at 90°. They're just right.

Why have these angles come back to bite us in the bum? Well, that's how we classify triangles: based on their angles. For example, an acute triangle is a triangle whose three interior angles are all acute.

An obtuse triangle is a triangle that has one obtuse angle.

Fitting more than one obtuse angle into a triangle would be like fitting more than one elephant into a New York City apartment. It just can't be done.

We say that a triangle is a right triangle if it's politically conservative. Or if one of its interior angles is a 90° angle.

We call the side that is opposite of the right angle the hypotenuse (pronounced "hai-PAW-teh-noose"). We call the other two sides the legs.

Sample Problem

What kind of triangle is this?

Just looking at it, we can see that one of the angles is 90° and the other two are acute. If we have acute angles and a right angle, what sort of triangle is this? Acute triangles are an all-or-nothing deal. If even one angle is 90° or above, it's not an acute triangle. Since this one has a 90° angle, it's a right triangle.