Angle Measures of Triangles
• A triangle is a figure formed by three segments joining three noncollinear points.
Classifying Triangles by Sides
• Equilateral Triangle
• Isosceles Triangle
• Scalene Triangle
• An equilateral triangle has three congruent sides.
• An isosceles triangle has at least two congruent sides.
• 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
• An equiangular triangle has three congruent angles.
• An acute triangle has three acute angles.
• A right triangle has one right angle.
• An obtuse triangle has one obtuse angle
Classify the triangle by its angles.
• 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
ΔABC is a right triangle. Find the measure of angle A.
• When the sides of a triangle are extended, other angles are formed.
• The three original angles are the interior 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.