Get down with the lingo
AAS Theorem
If two corresponding angles and one of the sides not between the angles in any two triangles are congruent, the two triangles are congruent.
Acute Triangle
A triangle that's slightly less cute than a-super-cute triangle. For that to be true, all the angles in the triangle have to be less than 90°.
Angle Sum Theorem
All the interior angles of a triangle add up to 180°. Always.
ASA Postulate
If two corresponding angles and the included side in any two triangles are congruent, the two triangles are congruent.
Congruence
When two objects are identical in every way. The only thing that separates them is a congruence transformation.
Congruence Transformation
These are transformations that create congruent figures once they're done, a.k.a. translation, rotation, and reflection. They're like little clone factories.
CPCTC
Stands for "Corresponding Parts of Congruent Triangles are Congruent." The "parts" we're talking about here are angles and sides, so don't go snooping at the local auto body shop.
Equilateral Triangle
A triangle with all three side lengths that are equal. All three angles are also equal (all are 60°). If it has three of anything else, they're equal too.
Exterior Angle
An angle supplementary to one of the triangle's inner angles. Just extend one of the sides of the triangle, and you'll see what we mean.
Exterior Angle Theorem
The measure of an exterior angle is equal to the sum of the measures of the remote interior angles. Even though it's an exterior theorem, you can use it indoors.
Hypotenuse-Leg Theorem
If the hypotenuses and corresponding legs of two right triangles are congruent, the two triangles are congruent. They've both gotta be right triangles though, or the deal's off.
Interior Angle
One of the inside angles in a triangle. They're innies, not outies.
Isosceles Triangle
A triangle with at least two congruent sides (or, from the Isosceles Triangle Theorem, two congruent angles).
Isosceles Triangle Theorem
Two sides of a triangle are congruent to each other only if the angles opposite the sides are congruent to each other. The sides and angles can go on double-dates.
Obtuse Triangle
A triangle that's a little slow on the uptake. Or one with an angle that's over 90°.
Remote Interior Angles
Two of a triangle's interior angles that aren't supplementary to a given exterior angle.
Right Triangle
A triangle that has an angle that's exactly 90°. Or possibly a triangle that's just never wrong about anything.
Scalene Triangle
A triangle whose three sides are all different lengths. He's probably just going through a growth spurt.
SAS Postulate
If two corresponding sides and the angle between the sides in any two triangles are congruent, the two triangles are congruent.
SSS Postulate
If all three sides in any two triangles are congruent, the two triangles are congruent. This is what gives triangles their rigid structure (but it won't make them any more emotionally stable).