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, mA + 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

CB

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.