1A QB Ch07 Introduction duction to Geometry.doc
- 1. 7 Introduction to Geometry 7 Introduction to Geometry Level 1 Questions (P01C07L03Q045) In the figure, (a) rewrite the names of the marked angles, (b) name all the line segments. Solution (a) a = PSQ or QSP b = RQS or SQR (b) PS, SR, RQ and QS (P01C07L03Q046) Write down the types of the marked angles in the figure. Solution a is an acute angle. b is a right angle. c is an obtuse angle. 1
- 2. Question Bank Update 1A d is a reflex angle. (P01C07L03Q047) Express the following angles in seconds. (a) 0.025 (b) 0.004 Solution (a) (b) (P01C07L03Q048) Express of a straight angle in degrees. Solution (P01C07L03Q049) In the figure, classify △ABC, △PQR and △XYZ according to (a) the sizes of their angles, (b) the lengths of their sides. Solution (a) △ABC is a right-angled triangle. △PQR is an obtuse-angled triangle. △XYZ is an acute-angled triangle. 2
- 3. 7 Introduction to Geometry (b) △ABC is a scalene triangle. △PQR is an isosceles triangle. △XYZ is an equilateral triangle. (P01C07L03Q050) In △XYZ, find p. Solution ∵ X + Y + Z = 180 ∴ p + 62 + 31 = 180 p = 180 62 31 = (P01C07L03Q051) In the figure, POQ is a straight line. Find POR. Solution ∵ POR + QOR = 180 ∴ POR + 52 = 180 POR = 180 52 = (P01C07L03Q052) In the figure, ABCD is a rectangle. Mark all parallel lines and perpendicular lines with suitable symbols. Solution 3
- 4. Question Bank Update 1A 4
- 5. 7 Introduction to Geometry (P01C07L03Q053) Using a ruler and a protractor, construct the above triangle. Solution (P01C07L03Q054) Using a ruler and a pair of compasses, construct the above triangle. Solution 5
- 6. Question Bank Update 1A (P01C07L03Q055) Write down the number of vertices, edges and faces for the following polyhedra. (a) (b) Solution (a) Number of vertices = Number of edges = Number of faces = (b) Number of vertices = Number of edges = Number of faces = (P01C07L03Q056) Draw the cross-section obtained when the following solids are cut at the dotted lines along the given planes. (a) (b) 6
- 7. 7 Introduction to Geometry Solution (a) (b) (P01C07L03Q057) Draw the uniform cross-sections of the following figures. (a) (b) Solution (a) (b) (P01C07L03Q058) Draw the 2-D representation of the following figure on an isometric grid paper. 7
- 8. Question Bank Update 1A Solution (P01C07L03Q059) Draw the 2-D representation of the following figure on an oblique grid paper. Solution 8
- 9. 7 Introduction to Geometry 9
- 10. Question Bank Update 1A Level 2 Questions (P01C07L04Q026) (a) Express in degrees. (b) Express in seconds. Solution (a) ∴ (b) ∴ (P01C07L04Q027) Without using a protractor, find the marked angle in each of the following clocks and express your answers in minutes. (a) (b) Solution (a) The marked angle 10
- 11. 7 Introduction to Geometry (b) The marked angle (P01C07L04Q028) Arrange right angle, round angle and straight angle in ascending order. Solution right angle round angle straight angle ∴ The above angles can be arranged in ascending order of their sizes as follows: right angle < straight angle < round angle (P01C07L04Q029) (a) Using a ruler and a protractor, construct △PQR with QR = 4 cm, PQ = 3 cm and PQR = 90. (b) Find the length of PR. (c) Classify △PQR by its angles. Solution (a) (b) (c) △PQR is a right-angled triangle. 11
- 12. Question Bank Update 1A (P01C07L04Q030) (a) Using a ruler and a pair of compasses, construct a circle with radius 1.5 cm. (b) Hence, using a ruler and a pair of compasses, construct an equilateral triangle PQR with side 3 cm on the figure obtained in (a). Solution (a) (b) (P01C07L04Q031) In △ABD, find x and y. Solution In △ABD, In △ABC, 12
- 13. 7 Introduction to Geometry (P01C07L04Q032) In the figure, △PQS and △PRT are right-angled triangles. Find a and b. Solution In △PQS, In △PQR, In △PRT, (P01C07L04Q033) Draw the 2-D representation of the following figure on an isometric grid paper. 13
- 14. Question Bank Update 1A Solution (P01C07L04Q034) Draw the 2-D representation of the following figure on an oblique grid paper. Solution 14
- 15. 7 Introduction to Geometry Level 2+ Questions (P01C07L05Q005) In the figure, PVS, UVR and QRST are straight lines. Find a, b and c. Solution In △RTU, In △RSV, In △PQS, 15
- 16. Question Bank Update 1A (P01C07L05Q006) (a) The 2-D representation of a solid is drawn on the above isometric grid paper. Draw the corresponding 2-D representation of the solid on an oblique grid paper. (b) Draw the uniform cross-section of the solid. Solution (a) (b) 16
- 17. 7 Introduction to Geometry Multiple Choice Questions (P01C07L06Q022) Which of the following angles is an obtuse angle? A. B. C. D. Solution A An obtuse angle is an angle between 90 and 180. (P01C07L06Q023) Which of the following angles is a reflex angle? A. 90° B. 150° C. 180° D. 190° Solution D A reflex angle is an angle between 180 and 360. (P01C07L06Q024) Express one-fifth of a right angle in minutes. A. B. C. D. Solution B 17
- 18. Question Bank Update 1A (P01C07L06Q025) From 2:30 p.m. to 9:30 p.m., what angle has the hour-hand of a clock turned? A. 180° B. 210° C. 240° D. 270° Solution B The hour-hand of a clock turns of a round angle every hour. Since there are 7 hours between 2:30 p.m. and 9:30 p.m., the hour-hand of a clock must turn of a round angle. of a round angle ∴ From 2:30 p.m. to 9:30 p.m., the hour-hand of a clock has turned 210°. (P01C07L06Q026) In the figure, DOG is a straight line. Name a supplement of FOG. A. EOD B. EOF C. DOF D. DOG Solution C Since FOG + DOF = DOG = 180, FOG and DOF are supplementary angles. (P01C07L06Q027) Which of the following sets of angles can be the interior angles of a triangle? 18
- 19. 7 Introduction to Geometry A. 15, 80, 95 B. 20, 56, 104 C. 30, 55, 85 D. 30, 70, 100 Solution B The sum of all interior angles of a triangle must be 180°. For option A, For option B, For option C, For option D, ∴ Option B can be the interior angles of a triangle. (P01C07L06Q028) In △PQR, find x. A. 32 B. 36 C. 40 D. 52 Solution A 19
- 20. Question Bank Update 1A (P01C07L06Q029) In the figure, BCD is a straight line. Find a. A. 38 B. 42 C. 48 D. 52 Solution D Since∠BCD is a straight angle, . Hence, . In △ABC, (P01C07L06Q030) Which of the following statements is/are correct? I. The sum of two acute angles can be a reflex angle. II. The sum of two obtuse angles can be a reflex angle. III. A triangle cannot have more than one obtuse interior angle. A. I only B. II only C. I and III only D. II and III only 20
- 21. 7 Introduction to Geometry Solution D For I, An acute angle must be less than 90. Thus, the sum of two acute angles should be less than 180, which is always less than the angle size of a reflex angle. So, I is incorrect. For II, An obtuse angle must be between 90 and 180. Thus, the sum of two obtuse angles should be between 180 and 360, which is the same as the angle size of a reflex angle. So, II is correct. For III, The sum of all interior angles of a triangle must be 180°. Since the sum of two obtuse angles is between 180 and 360, a triangle cannot have more than one obtuse interior angle. So, III is correct. (P01C07L06Q031) How many diagonals are in a quadrilateral? A. 1 B. 2 C. 3 D. 4 Solution B There are 2 diagonals in a quadrilateral. (P01C07L06Q032) Which of the following is/are the property/properties of a pentagon? I. It can be concave. II. It has five diagonals. III. It must have more than two obtuse angles. A. I and II only B. I and III only C. II and III only D. I, II and III 21
- 22. Question Bank Update 1A Solution A For I, A pentagon can have a reflex angle. So, it can be concave. So, I is correct. For II, A convex/concave pentagon has five diagonals (shown as dotted lines in the figure). So, II is correct. For III, A pentagon can have two obtuse angles only. For example, the interior angles of the following pentagon are 90, 90, 90, 135 and 135. So, III is incorrect. (P01C07L06Q033) The figure shows a circle with centre O and BOC is a diameter of the circle. Which of the following is/are correct? I. BC = 2OA II. △AOC is an isosceles triangle. III. The arc AMB is shorter than AB. A. II only B. I and II only C. II and III only D. None of the above. 22
- 23. 7 Introduction to Geometry Solution B For I, Since BC is a diameter and OA is a radius, BC = 2OA. For II, Since OA and OC are two radii of the circle, OA = OC. Thus, △AOC is an isosceles triangle. For III, The arc AMB is longer than AB. (P01C07L06Q034) Which of the following must be (a) regular polygon(s)? I. II. III. A. II only B. I and III only C. II and III only D. I, II and III Solution C For I, Since an equiangular quadrilateral is not necessarily an equilateral quadrilateral, I may not be a regular polygon. For II, The figure is a square which is a regular polygon. For III, The figure is an equilateral triangle which is a regular polygon. 23
- 24. Question Bank Update 1A (P01C07L06Q035) Which of the following is the cross-section obtained when the above figure is cut at the dotted line along the given plane? A. B. C. D. Solution D 24
- 25. 7 Introduction to Geometry (P01C07L06Q036) The figure shows a 2-D representation of a solid on an oblique grid paper. Which of the following is the solid? A. B. C. D. Solution B 25