Angles of Triangles

1
Angles of Triangles

• Angle Sum Theorem
• The sum of the measures of the angles of a
  triangle is 180 degrees.
• Third Angle Theorem
• If two angles of one triangle are congruent to
  two angles of a second triangle, then the third
  angles of the triangles are congruent.

2
Example 2-1b
Find the missing angle measures.
Answer

3
Angles of Triangles

• Exterior Angle An angle formed by one side of a
  triangle and an extension of another side.
• Remote Interior Angle The interior angles of a
  triangle not adjacent to a given exterior angle.
• Exterior Angle Theorem
• The measure of an exterior angle of a triangle is
  equal to the sum of the measures of two remote
  interior angles.

4
Example 2-2b
Find the measure of each numbered angle in the
figure.
Answer

5
Angles of Triangles

• Corollary A statement that can be easily proved
  using a theorem.
• Corollary 4.1
• The acute angles of a right triangle must be
  complementary.
• Corollary 4.2
• There can be at most one right or obtuse angle in
  a triangle.

6
Example 2-3b
Answer