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Classifying Triangles

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Classifying Triangles by Sides Equilateral ... Angles Theorem The measure of an exterior angle ... Triangle Obtuse Triangle Classify the triangle by its angles. – PowerPoint PPT presentation

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Title: 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.
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