Lesson 4. Classifying Triangles
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1 Lesson 4 Classifying Triangles Art Sculptures Sculptures are used as symbols for a message to those that view and admire the work. This sculpture is called Consophia and was created by Ian Lazarus to represent a sharing of knowledge and interaction between the United States and Canada. It is located in Odette Sculpture Park in Windsor, Ontario near the border between the United States and Canada. The sculpture is made of metal and has three main parts. There is a large triangle, a smaller triangle, and a large horizontal pipe that connects the triangles. It has Ojibway script writing on one side that translates to inspired interaction. The script on the other side translates to sharing knowledge. The triangles have two sides that are the same length. Reflection Read the lesson and determine the types of triangles that are used in this sculpture. 3-25
2 Objectives for this Lesson In this lesson you will explore the following concepts: Classify triangles by their sides Classify triangles by their angles Draw a specified triangle Classifying Triangles by Sides A triangle is made up of three line segments. These line segments are joined together at each endpoint. The endpoints of the line segments make up the triangle s vertices. Triangle Triangles can be classified by the length of their sides. Use the following Exploration to identify the three types of triangles based on their side measures. Let s Explore Exploration 1: Classifying Triangles by Sides Materials:, Lesson 4, Exploration 1 page in your Workbook, Centimetre Ruler, Pencil, Recording Device (optional) 3-26
3 1. Observe the following sets of triangles. Isosceles Triangles 3.2 cm 7.1 cm 7 cm Equilateral Triangles cm 6 cm 2 cm 2 cm 2 cm 6 cm Scalene Triangles cm cm 2.7 cm 3. 2 cm 4.1 cm 6 cm 3-27
4 For 2: Either record your answers or write them in your Workbook. If recording, follow the recording instructions in your Workbook. 2. What do the triangles in each set have in common? a. Isosceles triangles b. Equilateral triangles c. Scalene triangles 3. Use a centimetre ruler to identify the isosceles triangles in this set: A B C 4. Use a centimetre ruler to identify the equilateral triangles in this set: A B C 5. Use a centimetre ruler to identify the scalene triangles in this set: A B C 3-28
5 Example 1 Classify each triangle by its side lengths. a. b. c. 12 cm cm 1 a. No sides are congruent. This triangle is scalene. b. Two sides are congruent. This triangle is isosceles. c. All three sides are congruent. This triangle is equilateral. Go online to complete the Concept Capsule: Properties of Triangles. Classifying Triangles by Angles You can also classify triangles by the measure of their angles. There are three classifications: Acute Triangles, Obtuse Triangles, and Right Triangles. An acute triangle has three acute angles. You should recall that an acute angle is less than 90. Here are a few acute triangles: 3-29
6 The marks on the sides are used to help you know when sides are the same length. The first triangle has all acute angles and all three sides are the same. You can classify this triangle by its angles, which are all acute, and by its sides, which make it equilateral. That means every triangle can be classified in two ways: by the length of its sides and by its angles. Triangles Classified by Sides Scalene Isosceles Equilateral None of the sides are congruent. Two sides are congruent. Three sides are congruent. Triangles Classified by Angles Acute Obtuse Right All angles are acute. ( < 90 ) One angle is obtuse. ( > 90 ) One angle is right. ( = 90 ) 3-30
7 Example 2 Classify each triangle in two ways. a. b. c. a. This triangle has three different side lengths. It is scalene. All of the angles of this triangle are less than 90. It is acute. b. This triangle has two sides that are congruent. It is isosceles. All of the angles of this triangle are less than 90. It is acute. c. This triangle has two sides congruent so it is isosceles. One angle of this triangle is greater than 90. It is obtuse. Let s Explore Exploration 2: Obtuse and Right Triangles Materials:, Lesson 4, Exploration 2 page in your Workbook, Straws, String, Centimetre Ruler, Scissors, Protractor, Pencil For 1 5: Use the materials listed to help you answer the questions. 1. Can you create a triangle with two obtuse angles? Explain. 2. Can you create a triangle with two right angles? Explain. 3. Can you create a triangle that is isosceles and right? Explain. 4. Can you create a triangle that is equilateral and obtuse? Explain. 5. Can you create a triangle that is isosceles and obtuse? Explain. 3-31
8 Example 3 Draw a triangle that is right and scalene. 1. Make your right angle using a straight edge. Make the sides two different lengths. 2. Join the endpoints of the sides of the right angle. 3. Mark the right angle and each side. Let s Practice Turn in your Workbook to, Lesson 4 and complete 1 to
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acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
Warm-Up. Find the domain and range:
Warm-Up Find the domain and range: Geometry Vocabulary & Notation Point Name: Use only the capital letter, without any symbol. Line Name: Use any two points on the line with a line symbol above. AB Line
Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND
Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 1 AND Chapter 9 Geometry Copyright 2009 Pearson Education, Inc. Chapter 9 Section 1 Slide 2 WHAT YOU WILL LEARN Points, lines, planes, and