Classifying Triangles Angle Measures of Triangles

Triangle A triangle is a figure formed by three segments joining three noncollinear points.

Classifying Triangles by Sides Equilateral Triangle Isosceles Triangle Scalene Triangle

Equilateral Triangle An equilateral triangle has three congruent sides.

Isosceles Triangle An isosceles triangle has at least two congruent sides.

Scalene Triangle A scalene triangle has no congruent sides.

Classify the triangle by its sides.

Classification of Triangles by Angles Equiangular triangle Acute triangle Right triangle Obtuse triangle

Equiangular Triangle An equiangular triangle has three congruent angles.

Acute Triangle An acute triangle has three acute angles.

Right Triangle A right triangle has one right angle.

Obtuse Triangle An obtuse triangle has one obtuse angle

Classify the triangle by its angles.

Vertex A vertex of a triangle is a point that joins two sides of the triangle. The side across from an angle is the opposite side.

Name the side that is opposite the angle. Angle J Angle K Angle L

Triangle Sum Theorem The sum of the measures of the angles of a triangle is 180º. In ΔABC, m  A + m  B + m  C = 180º

Find the measure of the missing angle.

Corollary to the Triangle Sum Theorem The acute angles of a right triangle are complementary. In ΔABC, if m  C = 90º, then m  A + m  B= 90º A C B

ΔABC is a right triangle. Find the measure of angle A.

Interior Angles When the sides of a triangle are extended, other angles are formed. The three original angles are the interior angles.

Exterior Angles The angles that are adjacent to the interior angles are the exterior angles. It is common to show only one exterior angle at a vertex.

Exterior Angles Theorem The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles. m  1 = m  A + m  B

Find the measure of angle 1.