Classifying Triangles

1
Classifying Triangles

• Angle Measures of Triangles

2
Triangle

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

3
Classifying Triangles by Sides

• Equilateral Triangle
• Isosceles Triangle
• Scalene Triangle

4
Equilateral Triangle

• An equilateral triangle has three congruent sides.

5
Isosceles Triangle

• An isosceles triangle has at least two congruent
  sides.

6
Scalene Triangle

• A scalene triangle has no congruent sides.

7
Classify the triangle by its sides.
8
Classification of Triangles by Angles

• Equiangular triangle
• Acute triangle
• Right triangle
• Obtuse triangle

9
Equiangular Triangle

• An equiangular triangle has three congruent
  angles.

10
Acute Triangle

• An acute triangle has three acute angles.

11
Right Triangle

• A right triangle has one right angle.

12
Obtuse Triangle

• An obtuse triangle has one obtuse angle

13
Classify the triangle by its angles.
14
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.

15
Name the side that is opposite the angle.

• Angle J
• Angle K
• Angle L

16
Triangle Sum Theorem

• The sum of the measures of the angles of a
  triangle is 180º.
• In ?ABC, m?A m? B m? C 180º

17
Find the measure of the missing angle.
18
Corollary to the Triangle Sum Theorem

• The acute angles of a right triangle are
  complementary.
• In ?ABC, if m ? C 90º, then
• m ? A m? B 90º

A
B
C
19
?ABC is a right triangle. Find the measure of
angle A.
20
Interior Angles

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

21
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.

22
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

23
Find the measure of angle 1.