4Geometry an measures 4.1 Symmetry I an ientify refletion symmetry in 2D shapes ientify rotation symmetry in 2D shapes Example a i How many lines of symmetry oes this shape have? ii Colour two squares so that it has four lines of symmetry. b i What is the orer of rotational symmetry of this shape? ii Colour two squares so that it has rotational symmetry of orer four. Solution a i It has two lines of symmetry. They pass through opposite orners. ii Colour the other two orners.this will make the shape symmetrial horizontally an vertially as well as iagonally. The four lines of symmetry have been rawn on the shape. b i It has rotational symmetry of orer two. ii Colour the two squares as shown. The shape now has rotational symmetry of orer four. If you rotate the shape about the entre it will ome bak on itself four times in one omplete revolution. You an hek this with traing paper. 46 4 Geometry an measures 37686_P046_060.in 46 06/11/13 6:58 PM
Pratie questions 1 All of these shapes have line symmetry. Draw the lines of symmetry on eah shape. a b e f g h 2 Some of these shapes o not have line symmetry. Put a tik insie the shapes that have line symmetry. Put a ross insie those that o not. a b e f 3 If possible, a one extra square to give the shape a four lines of symmetry. b one line of symmetry. no lines of symmetry. Say if it is not possible. a b 4.1 Symmetry 47 37686_P046_060.in 47 06/11/13 6:58 PM
4 a Shae in squares to turn the ashe line into a line of symmetry. b Shae in squares to turn both the ashe lines into lines of symmetry. 5 Work out the orer of rotation symmetry of eah shape. a b Orer Orer Orer e f Orer Orer Orer 48 4 Geometry an measures 37686_P046_060.in 48 06/11/13 6:58 PM
6 Some shapes o not have rotation symmetry. Put a 1 insie shapes that o not have rotation symmetry. Write the orer of rotation symmetry insie the other shapes. a b e f g 7 Write own the orer of rotation symmetry of eah esign. a b e 8 Orer Orer Orer Orer Orer 8 Complete these shapes so they have rotation symmetry of the given orer about the entre shown. 9 a b Orer 2 Orer 4 Orer 3 Orer 2 4.1 Symmetry 49 37686_P046_060.in 49 06/11/13 6:58 PM
4.2 3D shapes I an ientify properties of 3D shapes Example This is a square-base pyrami. Work out the number of a faes b eges verties Solution a There is a square base an four triangular faes. There are five faes all together. b Two faes meet at an ege. There are four eges roun the base an four sloping eges. There are eight eges all together. There is a vertex at eah en of an ege. There are four verties roun the base an one more at the top. There are five verties all together. Pratie questions 1 This is a ube. Write own the number of a faes b eges verties 2 The shape of this wooen blok is a triangular prism. Work out the number of a faes b eges verties 3 This shape is an otaheron. It has eight triangular faes. a How many verties oes it have? b How many eges oes it have? 50 4 Geometry an measures 37686_P046_060.in 50 06/11/13 6:58 PM
4 A prism is slie into three parts. a Look at the yellow slie. Complete this sentene. The yellow slie has eges an verties. b Two of the faes of the yellow slie are squares. What shape are the other faes?. 5 All these shapes are hexagonal prisms. A hexagonal prism has eight faes. Two are hexagons. The other six are retangles. a How many verties oes a hexagonal prism have? b How many eges oes a hexagonal prism have? 6 Four ubes are balane one on top of the other. a How many square faes are ompletely visible? b How many square faes are not ompletely visible? 7 A pyrami is plae on top of a ube to make this shape. For this shape, work out the number of a verties b faes eges 4.2 3D shapes 51 37686_P046_060.in 51 06/11/13 6:58 PM
4.3 Measuring angles I an use a protrator to measure angles of any size Example a Draw this triangle. C b Measure angle C. Measure the length of BC. Solution A 26 6.3 m 103 B a Start by rawing AB. C Draw the angles at A an B. The lines ross at C. b Angle C is 51. The length of BC is 3.5 or 3.6 m. A B Pratie questions 1 Use a ruler an a protrator to make an aurate rawing of eah of the following triangles. Measure an label the thir angle. a 20 6 m 70 b 40 8.5 m 45 110 20 4.3 m 70 30 3.8 m 52 4 Geometry an measures 37686_P046_060.in 52 06/11/13 6:58 PM
2 Use a ruler an a protrator to make an aurate rawing of eah of the following triangles. Measure an label the other angles on your rawing. a 4 m b 5 m 40 4.7 m 55 8.3 m 3.1 m 120 7.2 m 5.3 m 6.8 m 70 3 Construt eah of the following triangles aurately on square paper. Remember to label all of the lines an angles. Measure the lines shown. a A b D N 4 m 5 m 6 m B 60 6 m C 110 E 5 m F L 50 5 m M AC = m DF = m NM = m C e Z f N A 70 4 m 50 B X 30 9 m 80 Y L 35 7 m 60 M CB = m XZ = m LN = m 4.3 Measuring angles 53 37686_P046_060.in 53
4.4 Calulating angles I an work out angles of a triangle work out angles roun a point Example Work out the sizes of angles a an b. Solution 115 an a are angles on a straight line. They a up to 180. a = 180-115 = 65 The three angles of a triangle a up to 180. 41 + 65 + b = 180 106 + b = 180 b = 180-106 = 74 41 b a 115 Pratie questions 1 Fin the missing angles. 120 100 a b 70 a = b = = 52 47 e 98 f = e = f = 54 4 Geometry an measures 37686_P046_060.in 54
2 Fin the missing angles. b 22 43 87 70 a 45 a = b = = 18 45 67 e 78 48 f = e = f = 3 Fin the missing angles. b 64 a 310 225 a = b = = e 72 96 f 251 = e = f = 4.4 Calulating angles 55 37686_P046_060.in 55
4 Fin the missing angles. 123 a 80 210 114 b 84 a = b = = 135 270 107 82 67 e f = e = f = 5 Fin the size of the angle marke by a letter in eah triangle. 60 70 30 40 120 a 100 b a = b = = 6 Fin the size of the unknown angles in eah isoseles triangle. 40 100 70 a 40 b 75 a = b = = = 56 4 Geometry an measures 37686_P046_060.in 56
4.5 Area an perimeter I an use the formula for the area of a retangle istinguish between area an perimeter Example This is the plan of the floor of a room. 11 m 3 m 4 m 5 m a Work out the area of the floor. b Work out the perimeter of the floor. Solution a There are two retangles. The area of the top retangle is 3 11 = 33 m 2. The area of the bottom retangle is 4 5 = 20 m 2. The total area is 33 + 20 = 53 m 2. The sies are in metres (m) so the area is in square metres (m 2 ). b There are two missing lengths. The right-han sie is 3 + 4 = 7 m. The other missing length is 11-5 = 6 m. The perimeter is the total length roun the ege of the room. The perimeter is 11 + 7 + 5 + 4 + 6 + 3 = 36 m. The sies are in metres so the perimeter is in metres. 4.5 Area an perimeter 57 37686_P046_060.in 57
Pratie questions 1 Work out the area of eah retangle using the formula A = l w. 1 a 7 m b 5 m 6 m 3 m 5 m 10 m A = m 2 A = m 2 A = m 2 8 m e 3 m f 10 m 4 m 3.5 m 11 m A = m 2 A = m 2 A = m 2 2 Work out the perimeter of eah retangle in Question 1. a b e f 3 The table shows the length an with of five retangles. Work out the area of eah retangle. Length With Area 7 m 11 m 4 m 15 m 10 m 25 m 13 km 4 km 12 m 32 m 58 4 Geometry an measures 37686_P046_060.in 58
4 These shapes have been ivie into retangles. Work out the area of eah retangle, then fin the total area of the shape. a 4 m b 3 m 5 m 7 m 8 m 3 m 2 m 12 m 3 m 8 m 4 m 5 m Area = m 2 Area = m 2 Area = m 2 5 Work out the perimeter of eah shape in Question 4. a b 6 Fin the unknown length or with for eah retangle. a? m b? m 8 m 6 m 24 m 2 4 m 30 m 2? m 10 m 64 m 2 54 m 2? m 7 m m m m 4.5 Area an perimeter 59 37686_P046_060.in 59
Comments, next steps, misoneptions 60 4 Geometry an measures 37686_P046_060.in 60