Alternate Angles. Clip 67. Mathswatch

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1 Clip 67 Alternate Angles ) Line PQ is parallel to line RS If angle PQR is equal to 6 a) What is the size of angle QRS? b) Give a reason for ou answer. P 6 Q R S ) Line DCE is parallel to line AB a) Find the size of angle ABC b) Find the size of angle DCA c) Calculate the size of angle ACB D C E A 68 B ) a) Find the size of angle DBF b) Find the size of angle HGC D E C 6 F B G H Page 6

2 Clips 68, 69 Angle Sum of Triangles - of ) Work out the size of the angles marked with letters. 0 b 0 70 a 00 0 c 0 d e f 6 7 ) Work out the size of the angles marked with letters. a b 70 7 c d 7 60 e f g 0 h i j j ) Work out the size of the angles marked with letters. 00 a b c 70 d f 0 e g Page 6

3 Clips 68, 69 ) ABC is a triangle. a) Find the size of angle A. Angle Sum of Triangles - of C 60 Diagram NOT accuratel drawn b) Triangle ABC is equilateral. Eplain wh. A 60 B ) BCD is a triangle. ABC is a straight line. Angle CBD = 70. BD = CD. a) (i) Work out the value of. D Diagram NOT accuratel drawn (ii) Give a reason for our answer. 70 A B C b) (i) Work out the value of. (ii) Give reasons for our answer. ) The diagram shows a -sided shape. All the sides of the shape are equal in length. a) (i) Find the value of. (ii) Give a reason for our answer. Diagram NOT accuratel drawn b) (i) Work out the value of. (ii) Eplain our answer. Page 6

4 Clip 70 Angles of Regular Polgons ) a) Work out the size of an eterior angle of a regular heagon. b) Work out the size of an interior angle of a regular heagon. ) a) Name the regular polgon, above. b) Work out the size of an eterior angle and of an interior angle for this polgon. ) The size of each eterior angle of a regular polgon is 90. Work out the number of sides of the regular polgon. ) The size of each eterior angle of a regular polgon is 0. Work out the number of sides of the regular polgon. ) The size of each interior angle of a regular polgon is 0. Work out the number of sides of the regular polgon. 6) The size of each interior angle of a regular polgon is 0. Work out the number of sides of the regular polgon. Page 6

5 Clip 7 Area of Circles ) Find the areas of the following shapes. Take to be. Diagrams NOT accuratel drawn a) b) c) cm m 8cm ) Work out the areas of the following shapes. a) mm b) 0cm ) The diagram shows a circular garden comprising a rectangular pond enclosed b grass. The circular garden has a diameter of 0 m. The rectangular pond measures 8 m b 6 m. Work out the area of the garden covered in grass. Take to be. and give our answer to the nearest m. 8 m 6 m ) The radius of the top of a circular table is 60 cm. The table also has a circular base with diameter 0 cm. a) Work out the area of the top of the table. b) Work out the area of the base of the table. ) The diagram shows a shape, made from a semi-circle and a rectangle. The diameter of the semi-circle is cm. The length of the rectangle is 7 cm. Calculate the area of the shape. Give our answer correct to significant figures. cm 7 cm Page 66

6 Clip 7 Circumference of Circles ) Find the circumference of the following shapes. Take to be.. Diagrams NOT accuratel drawn a) b) c) cm m 8 cm ) Work out the perimeter of the following shapes, taking to be.. a) mm b) 0 cm ) The radius of the top of a circular table is 60 cm. The table also has a circular base with diameter 0 cm. a) Work out the circumference of the top of the table. Let be. b) Work out the circumference of the base of the table. Let be. ) The diameter of a wheel on Kle s biccle is 0.7 m. a) Calculate the circumference of the wheel. Give our answer correct to decimal places. Kle ccles 000 metres. b) Using our answer in (a), calculate the number of complete turns the wheel makes. ) The diagram shows a shape, made from a semi-circle and a rectangle. The diameter of the semi-circle is cm. The length of the rectangle is cm. Calculate the perimeter of the shape. Give our answer correct to significant figures. cm cm Page 67

7 Clip 7 Area of Compound Shapes ) Find the area of each shape. a) b) cm 0 cm 0 cm cm cm 8 cm 8 cm cm cm c) d) m 6 m 6 mm 9 m mm 9 mm 6 mm mm ) Find the shaded area of each shape. a) b) cm cm cm 6 cm 7 cm 7 cm cm 0 cm c) d) 6 mm mm mm mm mm m 0 mm m Page 68

8 Clip 7 Rotations ) a) Rotate triangle T 90 anti-clockwise about the point (0, 0). Label our new triangle U b) Rotate triangle T 80 about the point (, 0). Label our new triangle V T O ) Describe full the single transformation which maps triangle T to triangle U. T U O Page 69

9 Clip 7 Reflections = - ) a) Reflect triangle T in the ais. Label our new triangle U. T b) Reflect triangle T in the line with equation = -. Label our new triangle V O ) a) Describe full the single transformation which maps triangle T to triangle U. T b) Describe full the single transformation which maps triangle T to triangle V O - - U - V - - Page 70

10 Clip 76 Enlargements ) a) Enlarge triangle T b scale factor using point (-, ) as the centre of enlargement. Label our new triangle U. b) Enlarge triangle V b scale factor a half using the point (-, -) as the centre of enlargement. Label our new triangle W. T O V - - ) Describe full the single transformation which maps triangle S to triangle T S O T Page 7

11 Clip 77 Translations ) - a) Translate triangle T b vector and label it U b) Translate triangle T b vector - and label it V 6 T O ) a) Describe full the single transformation which maps triangle A to triangle B. b) Describe full the single transformation which maps triangle A to triangle C. 6 A B O C Page 7

12 Clip 78 Find the Mid-Point of a Line ) Find the midpoint of A and B where A has coordinates (-, ) and B has coordinates (, -) O - - ) Find the midpoint of A and B where A has coordinates (, 0) and B has coordinates (8, 6). ) Find the midpoint of A and B where A has coordinates (-, -) and B has coordinates (, ). ) Find the midpoint of A and B where A has coordinates (-, -) and B has coordinates (7, ). ) Find the midpoint of A and B where A has coordinates (, -) and B has coordinates (7, ). 6) Find the midpoint of A and B where A has coordinates (-7, -) and B has coordinates (-, -). 7) The midpoint of A and B is at (, ). The coordinates of A are (-, ). Work out the coordinates of B. 8) The midpoint of A and B is at (.,.). The coordinates of A are (, ). Work out the coordinates of B. Page 7

13 Clip 79 Measuring and Drawing Angles ) Measure the following angles: a b d c e f ) Draw the following angles: a) angle ABC = 60 b) angle PQR = 7 c) angle XYZ = 7 X Q B A P Y Page 7

14 Clip 80 Drawing Triangles ) The diagram shows the sketch of triangle ABC. B Diagram NOT accuratel drawn 7. cm A 8. cm 8 C BC = 7. cm AC = 8. cm Angle C = 8 a) Make an accurate drawing of triangle ABC. b) Measure the size of angle A on our diagram. ) Use ruler and compasses to construct an equilateral triangle with sides of length 6 centimetres. You must show all construction lines. ) The diagram shows the sketch of triangle PQR. Q Diagram NOT accuratel drawn 0. cm 7. cm P 9 cm R a) Use ruler and compasses to make an accurate drawing of triangle PQR. b) Measure angle P. Page 7

15 Clip 8 Plans and Elevations The diagram shows a prism drawn on an isometric grid. Front a) On the grid below, draw the front elevation of the prism from the direction marked b the arrow. b) On the grid below draw a plan of the prism. Page 76

16 Clip 8 Nets ) Sketch nets of these solids. a) b) ) On squared paper draw accurate nets of these solids. a) Cube b) Cuboid cm cm cm cm 8 cm 6 cm c) Right-angled triangular prism d) Triangular prism cm cm cm cm 8 cm 7 cm 7 cm cm ) The two nets, below, are folded to make cubes. Two other vertices will meet at the the dot, A. Mark them with As. One other verte will meet the dot B. Mark it with B. a) A b) B Page 77

17 Clip 8 Smmetries ) Draw all the lines of smmetr on the triangle and the rectangle. ) What is the order of rotational smmetr of the two shapes below. S ) The diagram below, shows part of a shape. P The shape has rotational smmetr of order about point P. Complete the shape. ) On each of the shapes below, draw one plane of smmetr. Page 78