Lesson 10: Parts and Types of Triangles
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1 Lesson 10: Parts and Types of Triangles Learning Target: I can find the unknown angles and cite geometric justifications regarding angles in a triangle I can identify different types of triangles based on angles and sides Parts of a Triangle Each triangle has three and three. Each is where two sides meet. A pair of sides and the vertex define an, so each triangle includes three. Write "side" next to each side and circle the vertices on the triangle below. Each vertex is named with a letter. The sides can then be named with the letters of the two on either side of it. The triangle is named with a triangle symbol Δ in front followed by the three letters of its vertices. Label the vertices of the triangle at right with A, B, and C Name the 3 sides of this triangle Example 1. What is the name of the side shown in red?
2 Example 2. What is the name of the side shown in red? Example 3 Which of the following are names of this triangle? Types of Triangles Draw a picture Isosceles: The angles of an Isosceles triangle (and sides opposite them) are. Equilateral: Each angle/side of an equilateral triangle have measures. Each interior angle of an equilateral triangle would have a measure of degrees. Equilateral triangles are also called Equiangular ( when all angles are said to be equal) Scalene: The three angles/sides of a scalene triangle have measures. Right Triangle: A triangle that has one right angle
3 Lesson 10 Example 4. An isosceles triangle is an equilateral triangle. A. Sometimes B. Always C. Never M1 Example 5. Write true or false for the following statements A triangle can have more than one right angle. An equilateral triangle is also an isosceles triangle Example 6. This triangle is classified as. (Choose all that apply.) Triangle Sum Theorem In the past we have talked about how the interior angles of a triangle have a sum of 180..BUT WHY? In the diagram below, l m. l m What is the value of a? Reason: What is the value of b? Reason: What is the value of c? Reason: Triangle Sum Theorem: m a + m b + m c = The sum of the 3 angle measures of any triangle is.
4 Example 1. Find the measure of the missing angle. Example 2. What is the measurement of the missing angle? Example 3. In ΔABC, if m B is 84 and m C is 36, what is m A? Example 4. Solve for w, v and t m w = Give a reason for each answer: m v = m t = Example 5. Solve for 3, 4 and 5 m 3 = Give a reason for each answer: m 4 = m 5 = Example 6. Solve for x Find the measure of QRP and PQR
5 Lesson 10: Parts and Types of Triangles Problem Set Directions: For #1-5, solve for the variable (s). Give a reason that justifies your response for each variable. Remember, you may need to solve for other unknown angles, before you can solve for the specific variable that is asked. For Activities 1, 2 and 3, solve for all unknown angles. Give a reason for each answer
6 4. Solve for x. 5. What is the measure of B? 6. Solve for x and y in the diagrams. Explain why the equations you use to solve for x are appropriate and explain why they equations you used to solve for y are appropriate. Find the value of d and k: d = x =
7 4. The NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 10: Parts and Types of Triangles Homework For activities 1 and 2 find the missing angle. Explain your reasoning In the diagram of JEA at right, m JEA = 90 and m EAJ = 48. Line segment MS connects points M and S on the triangle, such that m EMS = 59. What is JSM? diagram at right shows ABD, with ABC, BE AD, and EBD CBD. If m ABE = 52, what is m D?
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