WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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7.1 Triangles Try These e.g., You will need • string • scissors • plain paper • a millimetre ruler • a protractor Try These Make a paper triangle. Draw a dot at each vertex. Cut the triangle so that each vertex is separate. Show that the sum of the angles is 1808. Cut three pieces of string that you can use to make a triangle. How many different triangles can you make 1. e.g., 1 Place your string on paper to make a triangle. Mark the vertices with a pencil. Join the vertices. 2 What are the side lengths e.g., 128 mm, 175 mm, and 184 mm 3 What are the angle measures e.g., 668, 748, and 408 ReflecTinG Suppose that the sum of the lengths of the two shortest sides is less than the length of the longest side. Can these three pieces of string make a triangle Explain. property a characteristic that is shared by all the members of a group 4 Two triangles are different if they are not congruent. Are any different triangles possible with your side lengths no 5 Compare your triangle with other students’ triangles. Could anyone make more than one triangle no Example 1 The bamboo stems in this photograph create an isosceles triangle. An isosceles triangle has two equal sides called legs. . The interior angles opposite the legs are also equal. MPS Do all isosceles triangles have these properties 1st pass Solution A. Find the midpoint of side AC. Label it M. Draw MB. A B M C B. What are the side lengths, in millimetres nABM : 19 mm, 50 mm, and 47 mm nCBM: 19 mm, 50 mm, and 47 mm 164 Apprenticeship and Workplace 12 NEL 8 Apprenticeship and Workplace 12 NEL
C. Is nABM congruent to nCBM How do you know Yes. e.g., They are congruent because only one triangle is possible with these sides. OR They are the same size and shape. D. Kate said that this property is a property of all isosceles triangles. Do you agree with Kate Explain. Include a diagram. • The angles opposite the equal legs are equal. e.g., Yes, I agree. If you draw a centre line, you get two congruent triangles. So the corresponding angles are equal. D D. e.g., E 20 mm 20 mm 45° M 45° 35 mm F Example 2 Pavlo is a carpenter. He uses triangular brackets for shelving. The sides of each bracket extend past the vertices to create exterior angles. What types of triangles have this property • Each exterior angle is 908 or greater. Solution A. Measure the interior and exterior angles in the acute triangle below. Record the angle measures on the diagram. Acute triangle: 105° Obtuse triangle: e.g., 90° 120° 150° 75° 35° 70° 110° 152° 48° 28° 132° 20° 145° 160° NEL B. Draw an obtuse triangle in Part A. Extend one side at each vertex to create three exterior angles. Measure the interior and exterior angles. Record the measures. Are any exterior angles acute yes C. Is the following a property of all triangles Explain. • Each exterior angle is 908 or greater. AW12SB 0176519637 No. e.g., One exterior angle on the obtuse triangle is less than 908. FN CO Technical Pass Approved Not Approved D. What triangles have the property in Part C NEL acute triangles and right triangles C07-F17-AW12SB CrowleArt Group 2nd pass ReflecTinG Why is showing that something is not a property easier than showing that it is a property Hint Use the triangular bracket above as an example of a right triangle. Chapter 7 Polygons 165 Chapter 7 Polygons 9
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WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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