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Angles of a Triangle Goals: · Classify triangles according to sides and to angles. · Apply the theorem and corollaries about the sum of the measures of the angles of a triangle. · Apply the theorem about the measure of an exterior angle of a triangle. Triangle - In small groups, write the definition of the following words: · · · · · · · Scalene Isosceles Equilateral Acute Obtuse Right Equiangular Scalene · No sides are congruent Isosceles · At least two sides are congruent Equilateral · All sides are congruent Acute · Three acute angles Obtuse · One obtuse angle Right · One right angle Equiangular · All angles are congruent Triangle Sum Theorem · The sum of the measures of the angles of a triangle is _______. Why? Corollary · A statement that can easily be proven by applying a theorem. Two Angles 3rd Angle Corollary · If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent. Equiangular Triangle Corollary · Each angle of an equiangular triangle has a measure of 60 degrees. Corollary 3 · In a triangle, there can be at most one right angle or obtuse angle. Corollary 4 · The acute angles of a right triangle are complementary. Remote Interior Angles Theorem · The measure of an exterior angle of a triangle equals the sum of the measure of the two remote interior angles Complete each statement with the word always, sometimes or never. 1. If a triangle is isosceles, then it is __________________ equilateral. 2. If a triangle is scalene, then it is _____________ isosceles. 3. If a triangle has two complementary angles, then it is ______________ a right triangle. In and an exterior angle at C is five times as large as Draw a picture and solve.