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Geometry Lesson 4-1: Apply Triangle Sum Properties Triangle: a polygon with three sides Interior angles: original angles (inside) Exterior angles: Angles that are linear pairs to interior angles Corollary to a theorem: The acute angles of a right triangle are complementary CLASSIFYING TRIANGLES BY SIDES Scalene Triangle Isosceles Triangle Equilateral Triangle NO congruent sides At least 2 congruent sides 3 congruent sides CLASSIFYING TRIANGLES BY ANGLES Acute Triangle Right Triangle Obtuse Triangle Equiangular Triangle *Notice that an equilateral triangle is also isosceles. *An equiangular triangle is also acute. 3 acute angles 1 right angel 1 obtuse angles 3 congruent angles Example 1: Classify ∆RST by its sides. Then determine if the triangle is a right triangle. 3-(-1) 4 -3-3 -6 -2 3 2-(-1) = 3 5-3 2 3 = -1 2 (Yes) THEOREM 4.1: TRIANGLE SUM THEOREM mA + mB + mC = 180 The sum of the measures of the interior angles of a triangle is 180. THEOREM 4.2: EXTERIOR ANGLE THEOREM m1 = m A + m B The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. Example 2: Use the diagram at the right to find the measure of DCB and 1. 3x-9 = x + 73 2x = 82 X = 41 3x + 16 = 2x + 52 -16 -16 X = 36 COROLLARY TO THE TRIANGLE SUM THEOREM mA + mB = 90 The acute angles of a right triangle are Complementary . Example 3: The front face of the wheelchair ramp shown forms a right triangle. The measure of one acute angle in the triangle is eight times the measure of the other. Find the measure of each acute angle. 8x + x = 90 X = 10 8 (10) = 80