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Classifying Triangles & Angles of Triangles Sections 4-1 & 4-2 A triangle is the figure formed by 3 segments joining 3 noncollinear points. Each of the 3 points is a vertex. The segments are the sides. Sides : AB, BC , CA Vertices : points A, B, C A C B Classifying Triangles by Sides Scalene Triangle – no sides congruent Isosceles Triangle – At least 2 sides congruen Equilateral Triangle – All sides congruent Classifying Triangles by Angles 700 500 Acute – 3 acute angles 600 Right – 1 right angle 400 1200 200 Obtuse – one obtuse angle 600 600 600 Equiangular – all angles congruent Parts of an Isosceles Triangle vertex angle leg base base angles leg Angle Sum Theorem The sum of the measures of the angles of a triangle is 180. 1000 400 400 Third Angle Theorem If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are congruent. Corollaries statements that can be easily proved using a theorem Each angle of an equiangular triangle has measure 60. In a triangle, there can be at most one right angle or obtuse angle. The acute angles of a right triangle are complementary. Exterior Angle Theorem The measure of an exterior angle of a triangle equals the sum of the measures of the 2 remote interior angles. Remote interior angles 350 Exterior 750 400 Joke Time What has wings and solves number problems? A mothematician What did one math book say to the other math book? Don’t bother me! I’ve got my own problems! What would a math student say to a fat parrot? Poly-no-mial