- Topics At a Glance
**Types of Triangles**- Properties of Triangles
**Classifying Triangles Based on Angles**- Classifying Triangles Based on Sides
- Congruence and Congruence Transformations
- Proving Congruence
- SSS and SAS
- ASA and AAS
- Isosceles Triangle Theorem and Hypotenuse-Leg Theorem
- Triangles on the Coordinate Plane

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*.

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.