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Name: Sha Tin College Mathematics Department Key Stage 4 CORE Level Course Unit 8 Assignment: Geometry Need to Know Angles on a line add to 180o Total /55 Angle Relationships Sketch the angle relationship here Angles at a point add to360o Vertically opposite angles are equal Angles in a triangle add to 180o Angles in an equilateral triangle are equal ie. 60o Base angles of isosceles triangles are equal Corresponding angles in parallel lines are equal Alternate angles in parallel lines are equal Co-interior angles in parallel lines add to 180o Complementary angles add to 90o Supplementary angles add to 180o Sum of exterior angles of “n” sided polygon is 360o Exterior angle of regular “n”sided polygon is 360o / n Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry 1 Sum of interior angles of “n” sided polygon is (n-2) x 180o Interior angle of regular “n” sided polygon is ((n-2)x 180o)/n The angle in a semi-circle is 90o The angle between a tangent and a radius of a circle is 90o Tangents from an external point are equal in length. A: Angle Relationships #1 NOT TO SCALE Two of the three line segments in the letter (a) Calculate the value of (i) (ii) (b) N shown in the diagram are parallel. p, Answer (a)(i) p = [1] Answer (a)(ii) q = [1] q. Mark the centre of rotational symmetry on the diagram, and label it O. [1] Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry 2 #2 NOT TO SCALE In the diagram WXYZ is a parallelogram. V is a point on XY. Angle WVZ = 90. Calculate the values of a, b and c. Answer a = b= c= [4] #3 NOT TO SCALE The diagram represents a church window, which consists of a rectangle surmounted by a semi-circle. The line through B and F is the line of symmetry, and BD is parallel to FG. Angle BAD 90 and angle ADB 30 . Calculate each of the following angles: ABD = DBF = BFG = BFH = GFH = [5] Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry 3 #4 In the diagram, EAB is parallel to DC. AE = AD, angle ABC 110 and angle EAD 52 . NOT TO SCALE (a) (b) What is the geometrical name of the quadrilateral ABCD? Answer (a) [1] Answer (b)(i) x = [1] Answer (b)(ii) y = [1] Answer (b)(iii) z = [1] Calculate the value of (i) (ii) (iii) x, y, z. Total for Section A /16 B: Angles in Polygons #1 A decagon is a polygon with ten sides. Calculate the interior angle of a regular decagon. Answer (a) Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry [3] 4 #2 The diagram shows the top of a table used for committee meetings. NOT TO SCALE XY is a line of symmetry, and BJIE is a straight line. CD is parallel to JI and to AL. BC is parallel to KJ. AB is parallel to LK. Angle BAL = 90, and angle CBJ = 30. (a) Calculate the size of each of the following interior angles marked in the polygon ABCDEFGHIJKL. Answer (a) [4] DEF = BCD = LKJ = KJI = (b) (i) Write down the size of each of the twelve interior angles of the polygon. Then find their sum. Answer (b)(i) Sum = (i) Find the value of the expression 180(n 2) , when n = 12. Answer (b)(ii) (ii) [2] [1] Comment on your answers to (b)(i) and (b)(ii). Answer (b)(ii) Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry [1] 5 #3 What is the size of an exterior angle of a regular nonagon? Answer ___________________ [2] Total for Section B /13 C: Angles in Circles #1 AD is a tangent to a circle, centre O. NOT TO SCALE BOC is a diameter. Given that angle ADB 35 , calculate (a) (b) angle BDO, Answer (a) [1] Answer (b) [1] angle ODC. Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry 6 #2 NOT TO SCALE RST is a tangent to circle, centre O. PS is a diameter. Q is a point on the circumference and PQT is a straight line. Angle QST = 37. Write down the values of a, b, c and d. Answer a = b= c= d= [4] #3 AOC and BOD are diameters of the circle, centre O. (a) If angle BDC 35 , calculate angle CAD. Answer (a) Angle CAD = (b) Draw the line of symmetry of the diagram. Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry [2] [1] 7 #4 NOT TO SCALE In the diagram ADE is a tangent to the circle, centre O. ABOC is a straight line, angle BAD 30 and AB = BD. Calculate (a) (b) angle CDE, Answer (a) Angle CDE = [2] Answer (b) Angle BCD = [2] angle BCD. Total for Section C /13 D:Symmetry, Similarity #1 (b) Eight of the interior angles of this star are right angles. What is the size of each of the eight interior (reflex) angles? Answer (b) (c) Draw the lines of symmetry on the star at the TOP of the page. (d) Write down the order of rotational symmetry of the star. Answer (d) Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry [3] [2] [1] 8 #2 The diagram shows a design made of four overlapping circles, each of radius 10 cm. Each centre is shown on the diagram. (a) On the diagram, draw the lines of symmetry of the design. (b) Give the order of rotational symmetry of the design. Answer (b) 2cm [2] [1] x #3 Triangles P and Q are similar. Calculate the length of side x. Answer ___________________ [2] Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry 9 #4 The bowls are similar. The diameter of the large bowl is 14cm, calculate the diameter of the small bowl. Answer ___________________ [2] Total for Section D /13 Check List for Unit 8 Geometry CAN DO STATEMENTS Unit 8 Geometry Main Learning Objectives RECAP (A) Know the meaning of these words with respect to Geometry. Acute, obtuse, right angle, reflex, parallel, perpendicular, equilateral, isosceles, regular, pentagon, hexagon, octagon, rectangle, square, kite, parallelogram, trapezium, Congruent NEW Know the meaning of these words with respect to Geometry. Similar, rhombus. RECAP (A) Be able to measure and draw angles in degrees. RECAP Be able to calculate missing angles by knowing the following angle properties. Angles round a point add to 360o, angles on a straight line add to 180o, vertically opposite angles are equal. RECAP Be able to calculate missing angles by knowing the following angle properties. Alternate angles on parallel lines are equal, corresponding angles on parallel lines are equal, co-interior angles on parallel lines are supplementary. RECAP Be able to calculate missing angles by knowing the following angle properties. Angles in a triangle add to 180o , base angles of isosceles triangles are equal. Tick RECAP Be able to calculate missing angles by knowing the following angle properties. Angle properties of a quadrilateral. RECAP Be able to calculate missing angles by knowing the following angle properties. Angle sum polygons. Find interior and exterior angles of regular and irregular polygons. NEW Be able to calculate missing angles by knowing that; the angle in a semi-circle is 90o Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Geometry 10