1 Classifying Triangles
Thurs, 3/6 SWBAT… classify triangles in the coordinate plane Agenda 1. Warm-up: (10 min) 2. Classifying triangles (40 min) Warm-Up: 1. Write your HW in your planners Homework: Isosceles and Equilateral Triangles #1 – #8 #9: Is the triangle scalene, isosceles, or equilateral A(0, 1), B(4, 1), C(7, 0) Unit 5: Classifying Triangles 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 angles and 3 straight sides. The three endpoints are called vertices. Classifying by side lengths Scalene Isosceles Equilateral Scalene Triangle All sides are different lengths. Isosceles Triangle Two out of the three sides are equal lengths. Isosceles Triangle Theorem If two sides of a triangle are congruent, then the angles opposite those sides are congruent. Ex. If AC = BC, name two congruent angles. Equilateral Triangle All sides have the same length Properties of Equilateral Triangles A triangle is equilateral if and only if it is has three congruent angles (all the measures would then be 600.) Ex. KLM is an equilateral triangle with KL = d + 2, LM = 12 – d, KM = 4d – 13. Find d and the measure of each side. 4d – 13 = d + 2 Substitution 3d – 13 = 2 Subtract d from each side. 3d = 15 Add 13 to each side. d = 5 Divide each side by 3. KL = 7, LM = 7, KM = 7 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. HW: Isosceles and Equilateral Triangles #1 – #8 #9: Is ABC scalene, isosceles, or equilateral A(0, 1), B(4, 1), C(7, 0) Using the ruler, draw triangles with the following side measures: a.) 3cm, 4cm, 6cm b.) 2cm, 2cm, 6cm Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Ex: Can these be the measures of a triangle? a.) 3cm, 4cm, 6cm b.) 2cm, 2cm, 6cm Example: Find value of x and missing side measurement Ex. Find the measure of each side of equilateral RST with RS = 2x + 2, ST = 3x, and TR = 5x – 4. 5x – 4 = 2x + 2 x=2 RS = 6 ST = 6 TR = 6 Ex. Find the measure of each side of isosceles ABC with AB = BC if AB = 4y, BC = 3y + 2, and AC = 3y. 3y + 2 = 4y y=2 AB = 8 BC = 8 AC = 6 Ex. Find x of isosceles right WZY if angle YWZ = 900, WZ = WY, and WYZ = 3x. 3x + 3x + 90 = 180 x = 15 Example: Find missing angle measurements 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. #1 – #4: Find x: 1.) 2.) 6x0 3.) 600 3x + 8 4x – 4 400 2x0 4.) (4x – 5)0 5.) Is triangle A(0, 1), B(4, 4), and C(7,0) scalene, isosceles or equilateral. Explain. SWBAT… classify triangles in the coordinate plane Mon, 3/10 Agenda 1. Warm-up: (10 min) 2. 4 Examples (25 min) 3. Review HW (10 min) Warm-Up: Find the missing angles: HW: Re-do 5 problems - Worksheet Warm-Up: What is Congruent? 1. AB ________ 2. BD _______ _______ _______ 3. CBE ________ BCE 4. BDE ________ 5. ABC ________ Example: Find missing angle measurements Name the missing coordinates of isosceles right triangle ABC. Answer: C(0, 0); A(0, d) Name the missing coordinates of isosceles right triangle SRQ. Answer: Q(0, 0); S(c, c) Find the missing angles. Warm-Up: Find the missing angles. Warm-Up Find the missing angles. Warm-Up: Find the missing angles. Homework: Collected. What do you know about the Pythagorean Theorem? 1. a) b) c) Formula? When and why it’s used? Solve for x:
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