Classify triangles by sides No congruent sides Scalene triangle At least two sides congruent Isosceles triangle Three congruent sides Equilateral triangle

Classify triangles by angles 3 acute angles Acute triangle 1 right angle Right triangle 1 obtuse angle Obtuse triangle 3 congruent angles Equiangular triangle

Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180 o.

Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary.

Base Angles Theorem If two sides of a triangle are congruent, then the angles opposite them are congruent.

Converse to Base Angles Theorem If two angles of a triangle are congruent, then the sides opposite them are congruent.

Corollary to Base Angles Theorem If a triangle is equilateral, then it is equiangular. Corollary to Base Angles Converse If a triangle is equiangular, then it is equilateral.

Triangle Inequalities (4) The largest angle is opposite the largest side. The largest side is opposite the largest angle. The smallest angle is opposite the smallest side. The smallest side is opposite the smallest angle.

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is larger than the third side of the second.

Converse of the Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.