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TOPIC 6-1: TRIANGLE BASICS TERM DESCRIPTION A plane, closed figure formed Triangle by 3 segments joining 3 noncollinear points. SKETCH A triangle is made up of three components: Q Vertices: Sides: R P Angles: One way to classify triangles is by the length of its sides. TERM DESCRIPTION SKETCH Scalene A triangle with no congruent sides. Isosceles A triangle with 1 pair of congruent sides. Equilateral A triangle with all three sides congruent. EXAMPLE 1 Classify each of the triangles by SIDES. a)_______________ b)_______________ c)_______________ The sum of the measures of the interior angles of a triangle is 180 . Triangles can also be classified by the measure of its interior angles. TERM DESCRIPTION A triangle in which all three angles have a measure less than 90° Acute Obtuse A triangle in which one angle has a measure greater than 90° Right A triangle in which one angle has a measure equal to 90° SKETCH A triangle in which all angles Equiangular are equal EXAMPLE 2 Classify the triangles by ANGLES. a)___________ b)___________ c)___________ 60 60 75 60 85 d)___________ 35 20 115 30 EXAMPLE 3 Find the measure of the third angle of a triangle, if the first angle has a measure of 66 and the second angle measures 37. EXAMPLE 4 Find the measure of each angle of RST. R 3x (x+40) x S T mR = __________ mS = __________ mT = __________ R EXAMPLE 5 Find the value of ‘x’. x x = __________ S x x T The triangle in EXAMPLE 5 is an equiangular triangle. Based on this example, we can say that each angle of an equiangular triangle is 60 . J EXAMPLE 6 Find the value of ‘x’. (3x+2) x = __________ K (2x+3) J and L in EXAMPLE 6 would be classified as acute angles. Since their sum is 90 , we can say that the acute angles of a right triangle are complementary. L An exterior angle of a triangle is formed by one side of the triangle, and the extension of an adjacent side. To find the measure of an exterior angle of a triangle, add the two remote interior angles. D EXAMPLE 7 Find the measure of 1. 80 1 2 E 40 F m 1 = ____________ EXAMPLE 8 In XYZ, mX = 63 and mZ = 64, find mZYR. Z X Y R m ZYR = ____________ EXAMPLE 9 In EFG, mG = (11x – 2) , mF = (8x + 4)°, and mFEH = (17x + 10)°. Find mF. F G E m F = ____________ H