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07-NelsonMathGr5-Chap07 6/24/04 2:47 PM Page 194 CHAPTER 7 3 Classifying Triangles by Angles A. Triangles can be classified as right-angled, obtuse-angled, or acute-angled triangles. Classify Teresa’s roof triangles by the sizes of their angles. You will need • a ruler • a protractor Goal B. Draw three roof triangles of different steepness. Investigate angle measures in triangles. Roofs have different shapes. Some roofs are steep so that snow slides off easily. C. Measure the three angles of each triangle. Label the angle measures. roof peak D. Classify your triangles by the sizes of their angles. E. How do the measures of the peak angles change as the roofs get steeper? does the angle at ? How the peak relate to the steepness of the roof? Teresa’s Solution right-angled triangle A triangle with one right angle Reflecting right angle The angle made by a square corner. A right angle measures 90º. 1. Which angle would you measure first to classify each triangle? Why? a) A acute-angled triangle A triangle with only acute angles I’ll draw roof triangles with different angles at the peak. Triangle A has a right angle. C 90° A Triangle B has an obtuse angle. It’s not as steep as triangle A. obtuse-angled triangle A triangle with one obtuse angle B obtuse angle An angle that measures greater than 90º F b) D E B The angles in triangle C are all acute angles. It’s steeper than triangles A and B. 135° c) acute angle An angle that measures less than 90º I H 2. Do you need to measure all three angles to classify a triangle? Explain your answer. C 45° 194 G NEL NEL 195 07-NelsonMathGr5-Chap07 6/24/04 2:47 PM Page 194 CHAPTER 7 3 Classifying Triangles by Angles A. Triangles can be classified as right-angled, obtuse-angled, or acute-angled triangles. Classify Teresa’s roof triangles by the sizes of their angles. You will need • a ruler • a protractor Goal B. Draw three roof triangles of different steepness. Investigate angle measures in triangles. Roofs have different shapes. Some roofs are steep so that snow slides off easily. C. Measure the three angles of each triangle. Label the angle measures. roof peak D. Classify your triangles by the sizes of their angles. E. How do the measures of the peak angles change as the roofs get steeper? does the angle at ? How the peak relate to the steepness of the roof? Teresa’s Solution right-angled triangle A triangle with one right angle Reflecting right angle The angle made by a square corner. A right angle measures 90º. 1. Which angle would you measure first to classify each triangle? Why? a) A acute-angled triangle A triangle with only acute angles I’ll draw roof triangles with different angles at the peak. Triangle A has a right angle. C 90° A Triangle B has an obtuse angle. It’s not as steep as triangle A. obtuse-angled triangle A triangle with one obtuse angle B obtuse angle An angle that measures greater than 90º F b) D E B The angles in triangle C are all acute angles. It’s steeper than triangles A and B. 135° c) acute angle An angle that measures less than 90º I H 2. Do you need to measure all three angles to classify a triangle? Explain your answer. C 45° 194 G NEL NEL 195 07-NelsonMathGr5-Chap07 6/24/04 2:47 PM Page 196 Curious Math Checking 3. a) What type of triangle has an angle that measures 120º and an angle that measures 30º? b) What type of triangle has an angle that measures 20º and an angle that measures 90º? Diagonal Angles 4. Classify the triangles by the sizes of their angles. Measure the angles if necessary. a) b) 1 2 3 4 5 6 E A B D F Measure and record the angles where the diagonals cross on the square and the other rectangle. H G C Angle Measures Square Practising 5. Kumiko’s class made triangle name tags for open house. Classify the triangles. a) c) A E B F C G D H Erlwanger d) Gorman 1 2 3 4 5 6 1 2 3 4 5 6 Li Draw two rectangles of different sizes and measure the angles where the diagonals cross. What conclusion can you make? 6. Look around the room. Find triangle shapes with different kinds of angles. a) Measure the sides and angles of the triangles. b) Draw the triangles. Label the angles. c) Classify the triangles according to their angle sizes. 7. Explain why you agree or disagree with each statement. a) Glynis said, “My triangle has one right angle, so it is a right-angled triangle.” b) Martin said, “My triangle has one acute angle, so it is an acute-angled triangle.” c) Jose said, “My triangle has one obtuse angle, so it is an obtuse-angled triangle.” 196 a) What do you notice about the angles where the diagonals of a square cross? b) What do you notice about the angles of the other rectangle? Johnson b) 1 2 3 4 5 6 Rectangle NEL NEL Measure the lengths of the diagonals in Question 1 from the vertex to the point where the diagonals cross. What do you notice? 197