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.

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Presentation transcript:

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.

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

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.

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

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.

Answer: Example 2-3b The piece of quilt fabric is in the shape of a right triangle. Find if is 62.