WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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Practice ReflecTinG Does it matter which side of a triangle you extend to make an exterior angle Explain. Hint Use the diagrams and definitions of different types of triangles in Getting Started. 1. Use your triangles from Example 2. a) The sum of the interior angle plus the exterior angle is the same at each vertex. What is this sum 1808 b) Why does it make sense that each vertex has the same sum When you extend one side, you create form a straight line . Angles that form have a sum of 1808 . two angles that a straight line c) Is this a property for all triangles Explain. • The sum of the interior angle plus the exterior angle is 1808. Yes. e.g., You always create an exterior angle by extending a side. The interior angle and exterior angle will always form a straight line. 2. Cables on the Esplanade Riel Bridge in Winnipeg illustrate many types of triangles. Circle the types of triangles that have each property. a) Some sides are equal. equilateral triangle isosceles triangle scalene triangle b) Some exterior angles are equal. equilateral triangle isosceles triangle scalene triangle c) No interior angles are equal. equilateral triangle isosceles triangle scalene triangle d) All three exterior angles are 908 or greater. acute triangle obtuse triangle right triangle e) Each exterior angle is equal to the sum of the interior angles at the other two vertices. acute triangle obtuse triangle right triangle 3. a) What is one property of isosceles triangles that is not a property of all triangles e.g., Isosceles triangles have exactly two equal sides. b) What is one property of isosceles triangles that is a property of all triangles e.g., The sum of the interior angles is 1808. 166 Apprenticeship and Workplace 12 NEL 10 Apprenticeship and Workplace 12 NEL
4. Use the angle measures to calculate the unknown angles in each triangle. Include interior angles and exterior angles. Record the measurements on the diagrams. 75° 105° 43° 1 32° 148° 137° 30° 60° 120° 2 30° 150° 150° 35° 145° 20° 3 125° 55° 160° 5. Use the triangles in Question 4. Complete this chart. Triangle 1 2 3 Sum of 3 interior angles 1808 1808 1808 Sum of 3 exterior angles 3608 3608 3608 Sum of 3 interior angles 1 sum of 3 exterior angles 5408 5408 5408 ReflecTinG Do you think that the sum of the interior angles and the exterior angles is the same for all triangles Explain. NEL NEL 6. Marcel’s crew builds A-frame cabins in Tofino. • The balcony is parallel to the base of a cabin. • The front of this cabin is an equilateral triangle. • The section above the balcony is also an equilateral triangle. Marcel wonders about this question. • Does drawing a line parallel to the base of any triangle create a second triangle with angles that are equal to those in the original triangle a) Test Marcel’s idea. • Draw a triangle. Draw a line through your triangle so that the line is parallel to the base. Are the angles in the small triangle equal to the angles in the large triangle yes b) Compare your results with a classmate’s results. Did your classmate get the same results yes c) Will adding a line that is parallel to the base always create a smaller triangle with the same angles Explain. AW12SB 0176519637 FN CO C07-F24-AW12SB CrowleArt Group 60° 60° 60° 60° 60° Hint One way to draw parallel lines is to draw along both sides of a ruler. 6. a) e.g., Yes. e.g., One angle is shared by both triangles. The other two angles are corresponding angles, formed by transversals that meet the parallel lines at the same angle. So each angle in the small triangle has a matching equal angle in the large triangle. 65° 25° 25° Chapter 7 Polygons 167 Chapter 7 Polygons 11
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WORKBOOK SAMPLER Chapter 7: Polygons - Nelson Education

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