Thomas Whitham Sixth Form

Thomas Whitham Sixth Form Geometry Workbook Mathematics S J Cooper Year 8 thomaswhitham.pbworks.com

Geometry () Constructions Name.. Do the following constructions within the spaces provided [practice first]. Perpendicular bisector of AB.. Bisector of angle ABC C A B A B. Perpendicular bisector of PQ.. Bisector of angle LMN. Q N P L M. Bisector of angle EDF.. The perpendicular from P to AB. E P A B D F 7. The perpendicular from X to JK. 8. Perpendicular bisector of JK. X J J K K

Geometry () Constructions Name.. Do the following constructions within the spaces provided [practice first] 9. Angle 0. Label Point R. 0. Angle ABC=90. Label point C P Q A B. Angle XYZ = 0. Label point Z.. Angle QPR =. Label point R. X Y P Q. Angle MLN = 0. Label point N.. Angle ABC =. Label point C. L M A B. Angle DEF = 7 Label point F.. Angle STU = 0. Label point S. D E T U

Geometry () Construction of triangles Remember do not remove any construction lines or arcs.. Draw a triangle ABC whose sides are AB = 7 cm, AC = cm and BC = cm. Measure and write down the size of angle A.. Draw a triangle LMN whose sides are LM = 9 cm, MN = cm and LN = 7 cm. Measure and write down the size of angle N.. Draw a triangle PQR whose sides are PQ = cm, PR = cm and QR = cm. Measure and write down the size of angle Q.. Draw a triangle DEF whose sides are DE = 8 cm, EF = cm and DF = 7 cm. Measure and write down the size of angle D.. Draw a triangle ABC whose sides are AB =. cm, AC =.7 cm and BC =. cm. Measure and write down the size of angle C.. Draw a triangle XYZ whose sides are XY = 7. cm, XZ =. cm and YZ = 9. cm. Measure and write down the size of angle Z. 7. Draw a triangle LMN whose sides are LM =.8 cm, MN =. cm and LN = cm. Measure and write down the size of angle N. 8. With the aid of compasses, protractor, rulers, etc... Draw accurately the following triangles and find the lengths required. (a) (b) Q (c) M cm cm E 0. cm 7. cm. cm cm R P. cm L 9. cm Angle E =? Angle P =? Angle M =? N cm

Geometry () Construction of triangles REMEMBER DO NOT REMOVE ANY CONSTRUCTION LINES OR ARCS. Use Pencil, Ruler, Compass and protractor for questions to.. Draw a triangle ABC whose side AB = 7 cm and angles BAC = 0 and ABC = 0 Measure and write down the length of side BC.. Draw a triangle XYZ, where XY = cm, ZXY = 70 and ZYX = 70. Measure and write down the length of ZX.. Draw a triangle DEF where DE = cm, EDF = and DEF =. Measure and write down the length of EF.. Draw a triangle PQR where PQ =. cm, PQR = and QPR = 7. Measure and write down the length of side QR.. Draw an accurate drawing of the triangle opposite. Use Pencil, Ruler and Compass only for questions to 0.. Draw a triangle PQR where PQ = cm, P and Qˆ R = 90 Q PˆR = 0.. cm 07 Measure and write down the length of side QR. 7. Draw a triangle BCD where BC = 8. cm, Measure and write down the length of side BD. B ĈD = and C Bˆ D = 0. 8. Draw a triangle HIJ where HI =.7 cm, I and ĤJ = 7 Measure and write down the length of side IJ. H. ÎJ = 0 9. Draw a triangle ABC where AB = cm, Measure and write down the length of side AC. A Bˆ C =0 and B ÂC = 0. 0. Draw a triangle DEF where DE = 7. cm, Measure and write down the length of side DF. E F = and Dˆ D ÊF = 0.

Geometry () Construction of triangles REMEMBER DO NOT REMOVE ANY CONSTRUCTION LINES OR ARCS. Use pencil, ruler, compass and protractor for questions to.. Draw a triangle LMN where LM = cm, Measure and write down the length of LN. LMN= ˆ 0 and MN = cm.. Draw the triangle PQR where PQ = 7 cm, Measure and write down the size of P Qˆ R. QPR ˆ = 70 and PR = cm.. Draw a triangle JKL where JK = cm, Measure and write down the length of JL. JKL ˆ = and KL =. cm.. Draw the triangle XYZ where XY =.8 cm, Measure and write down the size of Xˆ YZ. Yˆ XZ = and XZ =. cm.. Draw a triangle ABC where AB =. cm, ABC = and BC =. cm. Measure and write down the length of AC. Use pencil, ruler and compass only for questions to.. Draw the triangle DEF where DF =. cm, Measure and write down the size of FDE. D FˆE = 0 and FE =. cm. 7. Draw a triangle STU where ST = 0.7 cm, Measure and write down the length of TU. T ŜU = and SU = 8. cm. 8. Draw the triangle EFG where EF = 9. cm, Measure and write down the size of FG ˆ E. E FˆG = 0 and FG =.7 cm. 9. Draw the triangle PQR where PQ = 8. cm, P R = and QR =.7 cm. Qˆ Measure and write down the size of FG ˆ E. 0.Draw the triangle EFG where EF =. cm, Measure and write down the size of FG ˆ E. E FˆG = and FG =. cm.

. Construct rectangle ABCD where AB = 9 cm and BC = cm. State the length of the diagonal AC.. Construct a rectangle which has dimensions.cm by.7cm.. Construct rectangle LMNO where LM =.9 cm and MN =.8 cm. State the length of the diagonal MO.. Construct a rectangle which has dimensions 0.cm by.cm.

Geometry () Error in measurements In each of the following statements write down the limits between which each of the quantities can lie.. The length of a desk is 7 cm correct to the nearest cm.. The height of the desk is given as 9 inches correct to the nearest inch.. The length of the classroom is 700 mm correct to the nearest 00 mm.. The weight of John is 8 kg correct to the nearest kg.. The weight of Sarah is 0 pounds correct to the nearest 0 pounds.. Asif estimates the distance from his house to school is approximately two miles correct to the nearest mile. 7. The length of a rectangle is 9 cm correct to the nearest cm. 8. The width of the rectangle is given as 0 mm correct to the nearest mm. 9. The distance from Colne to Padiham is given as 900 m correct to the nearest 00m. 0. The distance from Burnley to Penzance is 800 miles correct to the nearest 0 miles.. The length of my lounge is feet correct to the nearest foot.. The weight of concrete block is 0 kg correct to the nearest 0 kg.. The volume of water in a bottle is 000 cm correct to the nearest 00 cm.. Freezing point is given as 0 C or F correct to the nearest F.. A recipe requires 0 grams of sugar correct to the nearest 0 grams.. The height of a standard door is m correct to the nearest 0 cm.

Geometry (7) Area & Perimeter of rectangles Work out (i) the area and (ii) the perimeter for each of the rectangles in to.... cm 8 cm cm cm 7 cm... cm cm 8cm 7cm 0cm cm cm 7. 8. 9. m m m m m m 0... 7mm 9m m m mm m 8cm. A photograph 8cm by cm is framed and hung on a wall. The frame is cm by 7cm.Calculate (a) The area of the photograph (b) The area of the frame (c) The area of the frame visible when the photograph is in place. 7cm cm cm

Geometry (8) Area of triangle Work out the area for each of the following triangles.... 7 cm 9 cm cm cm 8 cm... 7cm m m 8cm 7cm cm 0cm 7. 8. 9. mm m m 8mm m m 0. Find the heights of the following triangles. (a) Area = cm (b) Area = cm (c) Area = cm h cm h cm h cm cm cm cm (d) Area = 0 m (e) Area = 7 m (f) Area = 70 cm h m h m h cm m 9m cm

Geometry (9) Area of Irregular shapes. Work out (i) the area and (ii) perimeter for each of the following irregular shapes. (a) (b) (c) cm 8cm 7m cm 9cm cm cm m m 8m cm 8cm cm m 9m (d) cm (e) (f) 9 cm 8 cm cm cm 8 cm cm cm cm 9 cm cm 8 cm cm cm 7 cm cm. Work out the shaded area for each of the following: (a) cm (b) cm (c) cm cm (d) cm cm 8 cm 7 cm cm 7 cm cm cm 8 cm 9 cm cm (e) 8 cm cm cm cm cm 0 cm cm 7 cm cm 8 cm cm

. Work out the area for each of the following (all measurement are in cm): (a) (b) (c) 8 9 7 9 0 9 (d) (e) (f) 0 8 0 8 (g) 9 (h) (i) 8. Work out the shaded area for each of the following: (a) (b) (c) 8 7 9

. Find the area of the following irregular shapes. (a) (b) (c) 9cm cm cm cm 0cm cm cm 8cm (d) (e) (f) cm m m m cm m 7m 7cm

Geometry (0) Types of Polygons. Name each of the following types of triangles (a) (b) (c) (d) (e) (f). Draw a set of axes from to for each of the following problems. Plot the coordinates for each of the following. Join up the points to form the quadrilateral ABCD. What name is given to each shape drawn? (i) A(, ), B(, ), C(, ), D(, ) (ii) A(, ), B(, ), C(, ), D(, ) (iii) A(, ), B(, ), C(0, 0), D(, ) (iv) A(, ), B(0, ), C(, ), D(, ) (v) A(, ), B(, ), C(, ), D(, 0). (a) What name best describes a parallelogram with all angles at 90? (b) What name best describes a parallelogram with all sides equal in length? (c) What name best describes a parallelogram with all sides equal in length and all angles at 90?. Name each of the following quadrilaterals (a) BCDN A B C (b) JMHI (c) JMLK (d) DEFG K L N D E (e) DGHN (f) LKAB J M G F (g) LBNH I H

Geometry () Solids. For each of the tabulated solids below count the number of faces, vertices (corners) and edges. Enter the numbers in the appropriate place. In the last column work out the value of F + V E for each line. State what you notice. Number of Number of Number of F + V E Faces (F) Vertices (V) Edges (E) Cube Cuboid Square based pyramid Tetrahedron Triangular prism. A block of butter is in the shape of a cuboid until someone cuts away a corner with a knife, as shown. Count up faces, vertices and edges on the remainder of the butter shown. Complete the following. F =.. V =. E =. F + V E =.. (a) Using a pencil draw a sketch of a square based pyramid. Now take away the top corner using a rubber and redraw it to look as though someone had cut it away. (b) Complete the following for the remainder of the shape. F =.. V =. E =. F + V E =.. Here are some views of geometrical solids of the type drawn in class. State which they could be. [Some will have more than one answer!] (i) (ii) (iii) (iv)

. This is a cuboid (edges not equal in length) and shows a plane of symmetry. i) Use tracing paper to copy the outline and dotted (hidden) lines into your exercise book. On your diagram draw a different plane of symmetry. ii) Repeat the exercise in (i) and draw another different plane of symmetry.. This is a cube (all edges equal). It will have three planes of symmetry similar to the cuboid in question. Shown is another plane of symmetry. i) Use tracing paper to copy the outline and dotted lines into your exercise book. Draw a new plane of symmetry. ii) Repeat the exercise of (i) as many times as you need to until all planes of symmetry have been found. iii) How many planes of symmetry does the cube have? 7. This is a square based pyramid and shows a plane of symmetry. i) Use tracing paper to copy the outline and dotted lines into your exercise book. Draw a new plane of symmetry. ii) Repeat the exercise of (i) as many times as you can have until all planes of symmetry have been found. 8. This is a sphere with a plane of symmetry. Draw a sphere into your book along with another plane of symmetry. How many planes of symmetry could be drawn?

9. This is a cylinder with a plane of symmetry. Draw a cylinder into your book with a different plane of symmetry. How many planes of symmetry could be drawn? 0. (i) Using a square (side cm) complete a net for a square based pyramid each edge of which will be length cm. (ii) Draw on card a net for a square based pyramid of length cm. Add suitable flaps, cut out your net and glue together.. This is a sketch of a net for a regular tetrahedron, the dotted lines indicating folds. Construct on card an equilateral triangle of side 8 cm and mark the midpoints. Join the midpoints with dotted lines. Draw some flaps. Cut out your net; Use a pritt stick to glue together in the form of a regular tetrahedron, each edge of which should be of length cm.

Geometry () Angles. The straight line Work out the lettered angles for each of the following diagrams. Remember to show your working. All diagrams are not drawn to scale.... a 0 b 0 c... d 07 7 e 8 f 7. 8. 9. 0 h g 9 i 0 0... j 7 89 k m 77... m m n n n p p. 7. 8. 9. q 00 q r r r t t u u

Geometry () Angles. Angles at a point Work out the lettered angles for each of the following diagrams. Remember to show your working. All diagrams are not drawn to scale.... 80 a 0 b 00 90 9 c... 90 0 d 0 7 7 0 88 87 9 e f 7. 8. 9. 7 g 0 h 77 8 i i 9 0... k 8 k 7 m 88 m 7 n 7 n... q q 87 07 p 9 q 7 p r r r

Geometry () Opposite angles Work out the lettered angles for each of the following. Remember to show all working.... b d a 8 e c f g i 7 h... l k j m p 9 q 7. 8. 9. s 98 r u 0 t 0 7 v w 0... z z x x z y a e 8 d b c 8. f.. 79 m 8 n g q 9 k h n l 7 m m m p j 7 i

Geometry () Angles Corresponding angles Work out the lettered angles for each of the following. Remember to show all working.... a c b d 70 f 0 e... k h i 7 q p j g n m r 7. 8. 9. s t 8 w v u x 8 y z 0... b c a 9 e d 7 f 7 g 87 h... 79 0 m i j n p 7 r k q

Geometry () Angles Alternate angles Work out the missing angles in each of the following triangles. Remember to show your working. All diagrams are not drawn to scale.... 7 0 b c a e d... f h g 9 j i m k 98 7. 8. 9. n q 7 r s t v 8 u p 0... x w y z 7 a b

Geometry (7) Angles Angles in a triangle Work out the missing angles in each of the following triangles. Remember to show your working. All diagrams are not drawn to scale.... b 7 a 80 0 7 c... e f d 7 7 7 7. 8. 9. 8 h 77 g 7 i i 8 0... n m n k k+0 m+80 n. Two sides of a triangle measured and, what is the size of the third side?. Kamran measured the angles of a triangle as 9, 8 and 7. Are the measurements likely to be correct on this evidence?. In a right-angled triangle one angle is 8. What is the size of the other angle?. What are the sizes of the angles in a triangle with all equal angles? 7. The three angles in a triangle are given by x, x + and x +. What is the value of x?

Geometry (8) Angles. Work out the missing angles for each of the following: (a) (b) (c) a 7 8 0 b c g e f 9 (d) (e) (f) i 87 h k l 8 m. For each of the following isosceles triangles find the missing angles. (a) (b) (c) (d) a c b d 7 e f g h (e) 8 (f) k i j l 8. Calculate the missing angles for each of the following parallelograms (a) (b) (c) a 7 d e g b c f h i

(d) (e) p (f) j k n r q l 9 7 m (g) u s 9 t v (h) 9 x w 7. Showing your working determine which of the following are sets of parallel lines. (a) (b) (c) 8 8 8 (d) (e) 8 7

Geometry (9) Area of a circle Look at circle on the cm squared paper. Its radius r cm r 9 We estimate its area as follows: (i) Number of whole squares = cm (ii) Number of part squares = 0 cm Total = cm A Now using the calculator.88888.... 9 r 9 Record this information in your exercise book as shown above. Repeat this exercise for the other drawn circles and record the information in your book in the same way. When you have completed this task, draw up and complete a table as follows: Circle A.9 r What conclusion can you draw?

r= r= r=

Geometry (0) Area of a circle. Calculate the area for each of the following circles, giving your answers correct to decimal place. (a) (b) (c) (d) 8m cm cm 0m. Calculate the area of each of the following circles giving your answers correct to decimal places. (a) (b) (c) (d).m.cm 79m 0km. Which has the greater area, a circle with radius cm or a square with side cm?. Which has the greater area, a rectangle with dimensions m by m or a circle with diameter 0m?. Find the area of the semicircle drawn opposite, giving your answer to decimal places. cm. Find the area of the shape opposite, giving your 7 cm answer correct to decimal place. 7. Calculate the shaded area for each of the following shapes. [giving your answers correct to significant figures] 8 cm (a) (b) (c) cm 0cm m 9cm cm 8. A circle has an area of cm. Calculate the length of its radius, giving your answer to decimal places. cm

Geometry () Circumference of a circle. Calculate the circumference of each of the following circles, giving your answers correct to one decimal place. (a) (b) (c) (d) cm m 8cm m. Calculate the circumference of each of the following circles, giving your answers correct to decimal places. (a) (b) (c) (d).m.cm 79m 7m. Find the perimeter of the semicircle drawn opposite, giving your answer to decimal places. 0 cm. (a) What is the perimeter of a circle of diameter 0 metres (correct to decimal places)? The diagram is of a running track with straights of length 0m and with semicircular bends which have diameter 0m. (b) What is the length of one complete lap? 0m 0m (c) How many laps (approximately) must an athlete run in a race of 0 000m?. A bicycle wheel has diameter 80cm. Calculate its circumference, giving your answer correct to the nearest whole number.. What is the diameter of a circle whose circumference is cm? [Give your answer correct to decimal place]. 7. What is the area of a circle whose area is 0cm? {give your answer correct to the nearest whole number] 8. Which has the greatest perimeter, a circle with radius cm or a square with side cm?

Geometry () Volume of a prism. Without a calculator find (a) the base area (b) the volume for the following cuboids (i) (ii) (iii) (iv) cm m 7m m m cm cm 0m m m m m (v) (vi) (vii) (viii) m 9cm 9m 7cm cm cm 8cm 7cm m m m cm. A concrete beam is. metres long,. metres wide and. metres high. Find how many cubic metres of concrete was used to make the beam.. A classroom has a volume of respectively, how high is this classroom? 0 m, if the length and width of the room are 8m and 7.m. Bricks with dimensions cm by cm by 9cm are being used to build a wall. (a) Find the volume of one brick (i) in cm (ii) in m. (b) If the wall is to have a total volume of 0.7 m, how many brick will we need?. Without a calculator find the volume for each of the following triangular based prisms. (a) (b) (c) 7cm m cm 8m m cm cm cm (d) (e) (f) (g) cm cm m cm m 7cm 9cm m 7m cm cm 7m m

. Workout the volume for each of the following, giving your answers to decimal places. (a) (b) (c) (d) cm cm 7m 0cm cm 0cm (e) (f) (g) (h) m 7cm 9.m cm.m 7.cm 8.m cm m 8.cm 7. For each of the following calculate (i) the base area (ii) the volume, given that all measurements are in cm. (a) (b) (c) 9 9 0 7 7 (d) 9 8 7 8 (e) 0 0

Geometry () Reflections Exercise The dotted line is the mirror line. Draw the reflection of each object in the mirror line. Use a coloured pen to draw the image....... 7. 8. 9. 0......

Exercise. Draw the image of ABCD after a reflection in the -axis.. Draw the image of ABC after a reflection in the -axis. A D B C A B C - - - - - - - - - -. Draw the image of PQR after a reflection in the -axis. - - - - - - - - - -. Draw the following image after a reflection in the -axis. Q P R - - - - - -. Draw the following image after - - - - a reflection in the -axis. - - - - - -. Draw the following image after - - - - a reflection in the -axis. - - - - - - - - - - - - - - - - - - - -

7. Draw the image of the following after a reflection in the line. 8. Draw the image of the following after a reflection in the line - - - - - - 9. Draw the image of the following - - - - after a reflection in the line. - - - - - - 0. Draw the image of the following - - - - after a reflection in the line - - - - - -. Draw the image of the following - - - - after a reflection in the line. - - - - - -. Draw the image of the following - - - - after a reflection in the line - - - - - - - - - - - - - - - - - - - -

Geometry () Rotations Exercise In each of the following questions draw the image of the given object under a rotation about P and the angle described.. 90 anticlockwise. 80. 90 Clockwise P P P. 90 Clockwise. 80. 90 Anticlockwise P P P 7. 90 anticlockwise 8. 80 9. 90 Clockwise P P P 0. 90 Clockwise. 80. 80 P P P

Exercise. Draw the image of the following after a rotation of clockwise centre (0,0). Draw the image of the following after a rotation of centre (0, 0) - - - - - - - - - -. Draw the image of the following after a rotation of anticlockwise centre (0,0) - - - - - - - - - -. Draw the image of the following after a rotation of clockwise centre (, -) - - - - - - - - - -. Draw the image of the following after a rotation of clockwise centre (, ) - - - - - - - - - -. Draw the image of the following after a rotation of centre (, 0) - - - - - - - - - - - - - - - - - - - -

7. Draw the image of the following after a rotation of clockwise centre (, ) 8. Draw the image of the following after a rotation of centre (, -) - - - - - - - - - - - - - - - - - - - - 9. Draw the image of the following after a rotation of clockwise centre (, 0) 0. Draw the image of the following after a rotation of centre (, ) - - - - - - - - - -. Draw the image of the following after a rotation of anticlockwise centre (-, ) - - - - - - - - - -. Draw the image of the following after a rotation of clockwise centre (, ) - - - - - - - - - - - - - - - - - - - -

Geometry () Enlargements. Enlarge the shape below by a scale factor of three centre of enlargement O. Label the image P. O P. Draw shape ABCD after an enlargement with scale factor centre D. Label the image A B C D. D A B C. Enlarge the triangle LMN by a scale factor centre P. P L M N

. The object L has been enlarged onto Image L. (a) Identify the centre of enlargement and label it C. (b) State the scale factor of the enlargement. L L. Obtain the centre and scale factor of the enlargement drawn below.

Geometry () Enlargements TAKE CARE THAT PLENTY OF ROOM IS LEFT FOR THE FOLLOWING ENLARGEMENTS!. For each of the following state (i) the centre of enlargement (ii) the scale factor of the enlargement. (a) y 9 8 7 0 7 8 9 0 x (b) y 0 9 8 7 0 7 8 9 0 7 8 9 x

(c) y 9 8 7 0-9 -8-7 - - - - - 0 7 8 9 0 x (d) y -9-8 -7 - - - - - x 7 8 9 - - - - -. Enlarge LMN by a scale factor of centre (0, 0); Label the image L M N y L M N - - 0 7 8 x -

. Enlarge ABC by a scale factor of centre (, ). Label the image A B C y A B C - - 0 7 8 x -. Enlarge the object below with centre (, ) by a scale factor. y - - 0 7 8 x -. Enlarge the object by a scale factor of centre of enlargement (, ) y - - 0 7 8 x -. (a) Plot the points A(, ), B(, ) and C(, 0) and join up the points to form a triangle ABC. (b) Enlarge the triangle ABC by a scale factor of centre (, ) 7. (a) Plot the points P(, ), Q(, ) and R(, ) and join up the points to form a triangle PQR. (b) Enlarge the triangle PQR by a scale factor of centre (, )

Geometry (7) Translations. The diagram drawn opposite shows four triangles drawn in different positions. Using the vector notation describe the translation which will map (i) ABC onto EDG (ii) ABC onto HIJ (iii) ABC onto PQR (iv) PQR onto EDG (v) HIJ onto PQR A B - - - - - - P I J - Q C R - - - H E D G. Using the drawn triangle opposite A C - - - - - - - - - - B i) draw the image A B C after a translation of ii) iii) ABC by draw the image A B C after a translation of ABC by draw the image A B C after a translation of ABC by. (a) On a set of axes draw the shape STUV with coordinates S(, 0), T(, 0), U(, ) and V(, ). (b) Draw the image of STUV after a translation of. Label the image S T U V.. (a) On a set of axes draw the shape LMN with coordinates L(, ), M(, ), and N(, ). (b) Draw the image of LMN after a translation of (c) Draw the image of L M N after a translation of. Label the image L M N.. Label the image L M N 7

Geometry (8) Pythagoras Theorem. Work out the length of the hypotenuse for each of the following, giving your answers correct to decimal place. [all measurements are in centimetres] (a) (b) (c) a 7 b c 8 9 (d) (e) (f) d e 7 f 9 (g) (h) (i) (j) g h 0 i j 8 Work out the required lengths for each of the following, giving your answers to decimal places.. Find a. Find b cm 7cm a cm b 9cm. Find AC A. Find EF 0cm E cm D cm C cm B. Find PR 7. Find LM R P 7cm 7cm Q.m M F L.m N

8. Find p 9. Find x p.9cm 7 cm.cm A x 0cm 0. Find AC 9.8m C 0.m B. Find the length of the diagonal in the rectangle below: 0 cm. Find the sloped edge, XY, on the isosceles triangle drawn below. Z 0 cm 0 cm X 8 cm Y. A ladder is placed up against the side of a house so that it reaches a height of m. If the distance from the foot of the ladder to the base of the house is m, what is the length of the ladder?

Geometry (9) Pythagoras Theorem II. Work out the length of the lettered side for each of the following, giving your answers correct to decimal place. [all measurements are in centimetres] (a) (b) (c) 8 9 b c a (d) d (e) (f) 0 e f 7 (g) (h) 7 (i) (j) 0 g h 8 0 i j Work out the required lengths for each of the following, giving your answers to decimal places.. Find m. Find p p m cm cm cm cm. Find AB A. Find DE 0cm E cm D cm C 8cm B. Find PQ cm R 7. Find MN 8.m P 7cm Q M F L.7m N

8. Find c 9. Find x.cm.9cm cm c 9cm x J 0. Find JK 0.m L.m K. Find the height of the isosceles triangle drawn below. U cm cm h cm S 0 cm T. A ladder, of maximum length.m, is placed up against the side of a house. If the distance from the foot of the ladder to the base of the house is m, how high up the side of the house will the ladder reach?

Geometry (0) Bearings I. Write down the bearings of A from B for each of the following diagrams. (a) (b) N N A B B (c) A N (d) N A A B B (e) N (f) N A B B (g) N (h) N A B A B A

. Write down the bearings each of the following demonstrates (b) (b) N K Y J (c) N G X (d) N C F D (f) N (f) N S V T U (g) N (h) P N N M Q

Geometry () Bearings II. Draw an accurate diagram to represent each of the following bearings. (a) B is on a bearing of 0 from A (b) C is on a bearing of from D (c) L is on a bearing of 078 from M (d) H is on a bearing of from J (e) A is on a bearing of 97 from B (f) X is on a bearing of from Y (g) E is on a bearing of 9 from D (h) V is on a bearing of 97 from U (i) P is on a bearing of from Q (j) W is on a bearing of 8 from Z. Town B is km from town A on a bearing of 07. Town C is km from Town A on a bearing of. Using the scale cm represents km, draw a scale drawing to show Towns A, B and C. How far is town B from town C? On what bearing is town B from town C?. A ship, S, sails a distance of km on a bearing of 0 and then a further km on a bearing of 097. Using the scale of cm represents km, draw a scale drawing of this journey. How far is the ship away from its original position? On what bearing could the ship have originally taken?. The insert given shows the towns of Appleton, Barton, Cotley, Dove and Eccles. Using the diagram work out the bearing of (a) Eccles from Appleton (b) Cotley from Dove, (c) Dove from Barton, (d) Appleton from Cotley, (e) Barton from Eccles.. Using the second insert a ship is spotted from the two lighthouses shown. The first lighthouse, P, states that the ship is on a bearing of 08 while the second lighthouse, Q, states that the ship is on a bearing of. Using a suitable construction identify on the insert the position of the ship.

Geometry () Inserts Insert Appleton Barton Dove Eccles Cotley Insert P Q