Classifying Triangles Angle Measures of Triangles Triangle A

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.