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4.1 Triangles and Angles Triangles • Triangle-figure formed by 3 segments joining 3 noncollinear pts. • Triangles are named by these three pts (ΔQRS) R Q S Classifying Δs by Angles or Sides Angles • Acute • Obtuse • Right • Equiangular Sides • Scalene • Isosceles • Equilateral • Each of the three pts are vertices • Adjacent sides- 2 sides sharing a common vertex • Third side is opposite the given vertex. B A C Parts of a Right Triangle Leg Leg Parts of an Isosceles Triangle Leg __ ___ Base Leg How can ΔABC be right and isosceles? A B ____ _____ C Interior Angles A ))) B C Exterior Angles (formed by extending the sides) ( E D F Thm 4.1:Triangle Sum Thm • The sum of the measures of the interior angles of a triangle is 180o. A • mA + mB+ mC=180o B C Thm 4.2: Exterior Angles Thm • The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles. • m1=mA+ mB B A 1 C Corollary to triangle sum thm (Corollary- a statement easily proved using a thm.) * The acute angles of a right triangle are complementary. A A is comp. to C B C