Exploring Triangles. We can name triangles by the number of equal sides.
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1 UNIT 6 1 STUDENT BOOK Exploring Triangles LESSO N Quick Review At At Home Sc h o o l We can name triangles by the number of equal sides. An equilateral triangle has 3 equal sides. It has three 60 angles. It has 3 lines of symmetry. An isosceles triangle has 2 equal sides. It has 2 equal angles. It has 1 line of symmetry. A scalene triangle has no equal sides, no equal angles, and no lines of symmetry. Try These 1. Name each triangle as equilateral, isosceles, or scalene. a) b) c) d) e) f) 72
2 Practice 1. Write an S inside the triangles that are scalene. Write an I inside the triangles that are isosceles. Write an E inside the triangles that are equilateral. 2. a) Draw 3 different b) Draw 3 different equilateral isosceles triangles. triangles. Stretch Your Thinking Explain why it is not possible to make an equilateral triangle on a geoboard. 73
3 UNIT 6 2 STUDENT BOOK LESSO N Naming and Sorting Triangles by Angles Quick Review At At Home Sc h o o l An acute triangle A right triangle An obtuse triangle has all angles less has one 90 angle. has one angle greater than 90. D than 90. B I A C We can sort triangles in a Venn diagram. E F G 130 H Isosceles Triangles Right Triangles Try These 1. Name each triangle as an acute, a right, or an obtuse triangle. a) b) c) 2. Which triangle in question 1 is isosceles? How do you know? 74
4 Practice 1. Play this game with a partner. You will need pencils and an open paper clip to use as a pointer. Obtuse Player A spins the pointer and draws whichever triangle the pointer lands on. Player B takes a turn. Player B s triangle can touch, but not overlap. Continue taking turns. If you are unable to Acute Right Right Obtuse draw a triangle, you lose your turn. The last person to successfully draw a Acute triangle is the winner. Stretch Your Thinking Can you draw each triangle? a) A triangle with an obtuse angle and 2 equal sides. b) A triangle with a right angle and no equal sides. c) A triangle with 3 acute angles and 2 of the angles are equal. d) A triangle with 3 right angles. e) A triangle with 3 equal sides and 1 obtuse angle. 75
5 UNIT 6 3 STUDENT BOOK Drawing Triangles LESSO N Quick Review At At Home Sc h o o l You can use a ruler and a protractor to construct a triangle. Construct triangle ABC with these measures: AB = 3 cm A = 80 AC = 2.5 cm Sketch the triangle first. Label each side and angle. Draw side AB. Make it 3 cm long. Measure an 80 angle at A. Draw side AC. Make it 2.5 cm long. Join C to B to make side BC. C cm 80º A 3 cm B Try These 1. Use a ruler and protractor. Construct triangle EFG. Side EF is 7 cm long. Angle F is 90. Side FG is 5.3 cm long. 2. What is the measure of: a) angle E? b) angle G? 3. How long is side EG? 76
6 Practice 1. Construct each triangle using a ruler and a protractor. Label each triangle with the measures of all the sides and angles. a) Triangle JKL b) Triangle XYZ JL = 4 cm XY = 5.8 cm L = 60 X = 90 JK = 4 cm Y = 25 c) Triangle TUV d) Triangle PQR UV = 6.2 cm P = 70 T = 70 PQ = 3.5 cm U = 45 Q = 70 Stretch Your Thinking Suppose you double the side lengths of a regular triangle. What happens to the measure of the angles? Explain. 77
7 UNIT 6 4 STUDENT BOOK Investigating Polygons LESSO N Quick Review At At Home Sc h o o l A polygon is a closed shape with sides that are straight line segments. Exactly 2 sides meet at each vertex. The sides intersect only at the vertices. This shape is a polygon. These shapes are non-polygons. A regular polygon has all sides and all angles equal. It also has line symmetry. An irregular polygon does not have all sides equal and all angles equal. A convex polygon has all angles A concave polygon has at least less than 180. one angle greater than 180. Try These 1. Circle each polygon. 78
8 Practice 1. Match each shape to its description. a) regular polygon b) non-polygon c) concave quadrilateral d) convex quadrilateral 2. Draw a different shape that belongs in each set. a) b) Stretch Your Thinking Complete each polygon. a) a convex polygon b) a concave polygon c) a regular polygon 79
9 UNIT 6 5 STUDENT BOOK LESSO N Congruence in Regular Polygons Quick Review At At Home Sc h o o l Here are 2 ways to show 2 squares are congruent. Place one square on top of the other. If they match exactly, they are congruent. Compare the side and angle measures. If all sides are equal and all angles are equal, the squares are congruent. H 2 cm A D 2 cm 2 cm 2 cm 2 cm E G B 2 cm C 2 cm 2 cm F Try These 1. Triangles LMN and OPQ are congruent. Write the measure of each angle and the length of each side in OPQ. 3 cm 2. Which of these polygons are congruent? Explain how you know. L M N P O Q A B C D E F 80
10 Practice 1. Find pairs of congruent triangles. Join each pair with a line. A B C D E F G 2. Draw 3 congruent regular triangles. Label the angle measures and side lengths of each. Stretch Your Thinking Draw lines to divide this shape into 9 congruent triangles. 81
11 UNIT 6 7 STUDENT BOOK Perimeters of Polygons LESSO N Quick Review At At Home Sc h o o l We can find the perimeter of any polygon by adding the side lengths. For this pentagon: 4.0 cm 2.0 cm Perimeter cm The perimeter is 12 cm. 2.0 cm 2.5 cm We can use a formula to find the perimeter of some polygons. Square Parallelogram 2 cm 2 cm 3 cm P s 4 P 2 ( s) P 2 4 P 2 (3 2) The perimeters of the polygons are 8 cm and 10 cm. Try These 1. Find the perimeter of each polygon. a) b) 2.5 cm 82
12 Practice 1. Find the perimeter of each polygon. a) b) c) 2. Kerry skates laps around the playground. The playground is 150 m long and 50 m wide. How many laps will it take Kerry to skate 1 km? 3. The perimeter of an equilateral triangle is 5.1 m. How long are its sides? Give your answer in as many different units as you can. 4. The perimeter of an atlas is 1.4 m. How long might each side be? 5. Suppose the side lengths of a rectangle are halved. What would happen to the perimeter? Stretch Your Thinking One side of Kirby s rectangular garden measures 5 m. The perimeter of the garden is 27 m. Draw a sketch of Kirby s garden. Label the side lengths. 83
13 UNIT 6 8 STUDENT BOOK Area of a Rectangle LESSO N Quick Review At At Home Sc h o o l Here is one way to find the area of a rectangle. 8 cm Multiply the length by the width. 8 4 = 32 So, the area of the rectangle is 32 cm 2. 4 cm Rule: Formula: To find the area of a rectangle, multiply the length by the width. Area = length width A = w Try These Find the area of each rectangle. Complete the chart. A 7 cm 4 m B 6 m C Figure A B Area 3 m 7 cm D 11 m 2 m 5 cm E 20 cm 7 m C D E F 1 km F 10 km 84
14 Practice 1. Find the area of each rectangle. a) 5.5 km b) 4.0 m c) 4.0 km 0.9 m 5.0 cm 2.2 cm Area = Area = Area = 2. Measure the length and width of each object to the nearest unit. Use these dimensions to find the area. Record your work in the chart. Object a tabletop the classroom floor a sheet of paper a page from a magazine Length Width Area 3. Draw a rectangle with an area of 12 cm 2. Label the side lengths. Stretch Your Thinking Find the area of the shaded part of the rectangle. Show all your work. 4 cm 1 cm 6 cm 4 cm 85
15 UNIT 6 9 STUDENT BOOK LESSO N Volume of a Rectangular Prism Quick Review At At Home Sc h o o l You can use a formula to find the volume of a rectangular prism. The volume is the product of the prism s length, width, and height. Volume = length width height V = w h This rectangular prism is 7.0 cm long, 3.5 cm wide, and 2.3 cm high. Volume 7.0 cm 3.5 cm 2.3 cm 24.5 cm cm cm cm 7.0 cm 3.5 cm The volume of the prism is cm 3. Try These 1. Find the volume of each rectangular prism. a) b) c) 3.0 cm 2.0 cm 1.2 cm 0.5 cm 2.0 cm 4.0 cm 1.5 cm 1.5 cm 1.5 cm d) e) f) 1.2 cm 6 cm 2.0 cm 4 cm 6 cm 1.0 cm 1.5 cm 3.0 cm 0.5 cm 86
16 Practice 1. Find the volume of each box. a) b) c) 60 cm 1.0 m 2.4 m 5.0 m 30 cm 50 cm 25 cm 20 cm 40 cm 2. Work with a partner. a) Find 4 small boxes. Label the boxes A, B, C, and D. b) Measure the dimensions of each box. Estimate, then calculate, each volume. Record your results in the table. Estimated Actual Box Length Width Height Volume Volume A B C D 3. Complete each table. a) Length Width Height Volume b) (cm) (cm) (cm) (cm 3 ) Length Width Height Volume (cm) (cm) (cm) (cm 3 ) Stretch Your Thinking Jocelyn built a rectangular prism with 36 centimetre cubes. What might be the dimensions of the prism? Give as many answers as you can. 87
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