scalene triangle
triangle that has no congruent sides
isosceles triangle
triangle that only has 2 congruent sides
equilateral triangle
triangle that has 3 congruent sides, all sides are equal
acute triangle
triangle that has 3 acute angles
right triangle
triangle that has 1 right angle
obtuse triangle
triangle that has 1 obtuse angle
equiangular triangle
triangle that has 3 congruent angles
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180
Exterior Angles Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles
corollary
a statement that can be proved easily given using the theorem
Corollary to the Triangle Sum Theorem
The acute angles of a right triangle are complementary
Third Angles Theorem
If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent
SAS
If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent
Base Angles Theorem
If two sides of a triangle are congruent, then the angles opposite them are congruent
Converse of the Base Angles Theorem
If two angles of a triangle are congruent, then the sides opposite of them are congruent
Corollary to the Base Angles Theorem
If a triangle is equilateral, then it is equiangular
Corollary to the Converse of the Base Angles Theorem
If a triangle is equiangular, then it is equilateral
SSS
If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent
included side
the common side of two consecutive angles in a polygon
ASA
If two angles and the included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent
AAS
If two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of a second triangle, then the two triangles are congruent
CPCTC
Corresponding Parts of Congruent Triangles are Congruent
coordinate proof
involves placing geometric figures on axes
legs
two congruent sides of an isosceles triangle
vertex angle
angle formed by the legs
base
third side of an isosceles triangle
base angles
two angles adjacent to the base