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5.1 Classifying Triangles SWBAT classify triangles in the coordinate plane Classification means put things into a group according to how they are alike. We will break this group of animals into smaller groups. The same animals can be put into different groups depending on what we look at when we classify them. Today you will learn how triangles can be classified in two different ways... Think of all the different kinds of triangles you know. Did you come up with all of these? Acute Obtuse Right Scalene Isosceles Equilateral Triangle A polygon with 3 sides. The three endpoints are called vertices. Classifying by side lengths Scalene Isosceles Equilateral Scalene Triangle All sides are different lengths. Isosceles Triangle At least two out of the three sides are equal lengths. Equilateral Triangle All sides have the same length Classify this triangle by its sides. Classify this triangle by its sides. Classify this triangle by its sides. Classify the following triangles by their sides. Use these signals: Scalene Isosceles Equilateral Classify by sides. Give the best name. Scalene Isosceles Equilateral Classify by sides. Give the best name. Scalene Isosceles Equilateral Classify by sides. Give the best name. Scalene Isosceles Equilateral What formula do you use to determine if a triangle is scalene, isosceles, or equilateral? Answer: The terms scalene, isosceles, and equilateral have to do with side lengths of a triangle so you use the Distance Formula. Classifying by angle measures Right Acute Obtuse Acute Triangle All three angles are less than 900. 800 400 600 Obtuse Triangle One of the three angles is more than 900 200 1300 300 Right Triangle One of the three angles is exactly 900 Classify the following triangles by their sides. Use these signals: Acute Obtuse Right Classify by angles. Acute Obtuse Right Classify by angles. 1000 Acute Obtuse Right Classify by angles. 850 450 500 Acute Obtuse Right B A D C E Now you should be able to classify any triangle by both its side lengths and its angles. Classify the triangles by sides lengths and angles a) b) 7 c) 40° 15° 25 24 70° 70° 120° Solutions: a) Scalene, Right b) Isosceles, Acute c) Scalene, Obtuse 45° Example 1 Classify a triangle in a coordinate plane Determine whether PQO with vertices at P(-1, 2), Q(6, 3), O(0, 0), is scalene, isosceles, or equilateral. Explain. SOLUTION Use the distance formula to find the side lengths. OP = = ( x2 – x1 ) 2 + ( y2 – y1 ) 2 ( (– 1 ) – 0 ) 2 + ( 2 – 0 ) 2 = 5 2.2 = 45 6.7 ( 6 – (– 1 )) 2 + ( 3 – 2 ) 2 = 50 7.1 OQ = ( x2 – x1 ) 2 + ( y2 – y1 ) 2 = PQ = ( 6 – 0 )2 + ( 3 – 0 )2 ( x2 – x1 ) 2 + ( y2 – y1 ) 2 = EXAMPLE Explanation Classify a triangle in a coordinate plane (continued) PQO is a scalene triangle since none of the sides are congruent. Determine whether PQO with vertices at P(-1, 2), Q(6, 3), O(0, 0), is scalene, isosceles, or equilateral. Explain. Ex: Identify the indicated triangles in the figure. a. isosceles triangles Answer: ADE, ABE b. scalene triangles Answer: ABC, BCE, BDE, CDE, ACD, ABD c. equilateral triangles Answer: None! Exit Slip Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain. Answer: AB = 5 BC = 5 CA = 7.1 Since AB = Triangle ABC is isosceles since two of the sides are congruent. Triangle Sum Theorem The sum of the measures of the angles of a triangle is 180° x y x + y + z = 180 z Find the missing angles. 1) 2) x 26° y 35° 31° 65° 3) y° x° 4) 82° x° 70° 30° 1)80 2) 123 3) x = 60, y = 20 4) x = 57, y = 57, z = 82 41° y° z° Example: The measures of the angles of a triangle are in the ratio 1:3:5. Find the measure of each angle. x + 3x + 4x = 180 8x = 180 x = 22.5 Plug in to find each angle: 1(22.5)= 22.5° 3(22.5) = 67.5° 4(22.5) = 90° 3x x 4x