Section 4.1: Triangle Classification (Review) Classifying Triangles By Sides: • Scalene no congruent sides • Isosceles at least 2 congruent sides • Equilateral 3 congruent sides Classifying Triangles By Angles: • Acute 3 acute angles • Right 1 right angle • Obtuse 1 obtuse angle • Equiangular 3 congruent angles Hypotenuse: the opposite side of the right angle Legs:the sides that form the right angle of a right triangle the congruent sides of an isosceles triangle leg hypotenuse leg leg leg base In an isosceles triangle, we refer to the base and the legs. base angles are also congruent Base Angles Theorem: If 2 sides of a triangle are congruent, then the angles opposite them are congruent. Converse of Base Angles Theorem: If ... Triangle Sum Theorem: sum of measures of the interior angles of a triangle is 180O. Exterior Angle Theorem: the measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles Exterior Angles Fact: 0 the sum of the exterior angles of a triangle is 360 Exterior Angles An exterior angle forms a linear pair with its adjacent interior angle, so they sum to what? Interior Anlges Prove the Triangle Sum Theorem: B 2 Given: ΔABC Prove: m<1 + m<2 + m<3 = 180 A 3 1 Corollary to the Triangle Sum Theorem: The acute angles of a right triangle are complementary. A m<A + m<B = 90 o B Ex. Solve for x. 3x0 (2x 15)0 C Examples: Solve for x. b) a) (5x + 4)0 (4x 8)0 360 420 77 0 c) x0 2x0 (4x + 8)0 d) An equilateral triangle has 1 angle measure of 4x0. What is the value of x? e) In triangle ABC, m<A=42. The measure of <B is 8 less than twice m<A. What is the measure of the exterior angle at vertex C?