Math topic中文

Properties shapes

properties of triangles, special quadrilaterals and regular polygons (pentagon, hexagon, octagon and decagon), including symmetry properties

Practice questions

  1. 1The figure is made up of a regular pentagon ABCDE and a regular hexagon CDFGHI. Find angle BCI. Answer ... ° Determine w…
  2. 2It is given that ξ={x:x is polygon},\xi = \{x: x \text{ is polygon}\}, p={x:x is a parallelogram},p = \{x: x \text{ is a parallelogram}\}, q={x:x is a quadrilateral},q = \{x: x \text{ is a quadrilateral}\},…
  3. 3In the diagram, POR is a quadrant of a circle with radius 6 cm. OR and PQ are parallel. QR is an arc of a circle with ce…
  4. 4下列命题中，正确的个数是()(1)()(1)三点确定一个圆； (2)平分弦的直径垂直于弦； (3)相等的圆心角所对的弧相等； (4)正五边形是轴对称图形． A. 11个 B. 22个 C. 33个 D. 44个
  5. 5A circle with centre O has a tangent XY at D. ∠ODC = 70°, ∠BCD = 120° and ∠ODA = 15°. Find ∠CDY. Find ∠DAB. Find ∠OBA. T…
  6. 6In the diagram, PQRS is a vertical rectangular wall of height 2.5 m and length 7.5 m. T is a point on level ground from…
  7. 7In the diagram ABCDE is a regular pentagon. BE and BD are straight lines. Find, giving reasons for each answer, angle AB…
  8. 8A, B and C are points on the circle with centre O. Q and R are points on the circle with centre P. CSR and BSQ are tange…
  9. 9一个正多边形绕它的中心旋转45°后，就与原正多边形第一次重合，那么这个正多边形（ ） A. 是轴对称图形，但不是中心对称图形 B. 是中心对称图形，但不是轴对称图形 C. 既是轴对称图形，又是中心对称图形 D. 既不是轴对称图形，也不是中心…
  10. 10In triangle ABC, AB = 14.6 cm, BC = 7.6 cm and angle BAC = 31°. Find obtuse angle ACB. Answer ...° area of triangle ABC.…
  11. 11In the diagram, AB is a tangent to the circle with centre O, ∠CAB = 58° and CDE is a straight line. Find, stating your r…
  12. 12The diagram shows two circles that touch at C. A, B and C are points on the small circle, centre P. C, D and E are point…
  13. 13In the diagram, ABCDEFGH is a cuboid with dimensions 8 cm by 6 cm by 15 cm. V is the centre of the rectangular base. Sho…
  14. 14In the diagram, A(1, 2), B(8, 5), C(13, 7) and D(13, 2) are four points. Show that AB+BC=13.0AB + BC = 13.0, correct to 3 signif…
  15. 15In the diagram, OABC is a parallelogram and D is the midpoint of BC. BE and OC produced intersect at point F. It is give…
  16. 16The points A, B, E and D lie on the circle with centre O. BEC is a straight line and BF is a tangent to the circle at po…
  17. 17A rhombus PQRS is drawn on a square grid. Draw square RSTU on the grid such that RSTU does not overlap with PQRS. Using…
  18. 18The diagram below shows part of a regular 18-sided polygon, ABCDEF... The lines BC and ED are extended to meet at the po…
  19. 19一个多边形的每一个外角都是72°，则这个多边形是（ ） A. 正方形 B. 正五边形 C. 正六方形 D. 正七边形
  20. 20ABCD is a square and AQ is perpendicular to PR. PQR and ADR are straight lines. DQ : DC = 1 : 2. Show that triangle DQR…
  21. 21The diagram above shows a kite ABCD where angle BAC = 30°. EB, BD and DF are three sides of a regular polygon. ABE and A…
  22. 22The scale of a map is 5 cm : 1 km. A reservoir has an actual area of 0.7 km^2. Find the area, in square centimetres, of…
  23. 23In the diagram, ABCD is a rectangle. OAB is a sector of a circle, centre O. OXD and OYC are straight lines. Show that tr…
  24. 24ABCD is a parallelogram. A is the point (−6,−2)(-6,-2) and B is the point (−4,−7)(-4,-7). BC→=(8−2)\overrightarrow{BC} = \begin{pmatrix}8\\-2\end{pmatrix}…
  25. 25请先找出正三边形、正四边形、正五边形等正多边形的对称轴的条数，再猜想正n边形对称轴的条数为 ．
  26. 26In the diagram, a wooden ramp is shown where ∠BCF=90∘\angle BCF = 90^\circ and ∠CBF=35∘\angle CBF = 35^\circ. ABCD, CDEF and ABFE ar…
  27. 27It is given that PQ→=(−56)\overrightarrow{PQ}=\begin{pmatrix}-5\\6\end{pmatrix} and the position vector of PP is (2−4)\begin{pmatrix}2\\-4\end{pmatrix}…
  28. 28In the parallelogram PQRS, QR = 12.7 cm and angle PQR = 50°. Show that the length of RS = 5.407 cm. Answer Hence or othe…
  29. 29The angles of a quadrilateral taken in order are 3xx, 6xx, 5xx and 4xx. Find the value of xx. Answer xx = ___ Expl…
  30. 30PQRS are points on the circumference of a circle, centre O. Angle OQR = 50°, angle PSR = 73° and obtuse angle SOQ = 156°…
  31. 31In the diagram, ABC is an equilateral triangle, ACDE is a square and angle FAC = 15°. Show that triangle EAF and triangl…
  32. 32The diagram shows a rectangular table ABCD arranged such that the side AD is inclined at an angle of θ\theta to the wal…
  33. 33A regular polygon has interior angles of 140°. Find the number of sides of the polygon The diagram shows a sketch of a r…
  34. 34The ratio of the area of a regular hexagon : area of an equilateral triangle = 49 : 9. Show that the ratio of the perime…
  35. 35In the diagram, A, B, C and D are four points on a circle, centre O. Angle ABO=x∘ABO = x^\circ and angle ADO=y∘ADO = y^\circ. Fi…
  36. 36B, C, D, E and F are points on the circle with centre O. AE is tangent to the circle and ABC is a straight line. ∠BAE=38∘\angle BAE = 38^\circ…
  37. 37O is the centre of the circle passing through B, E, D and C. Angle DOC=84∘DOC = 84^\circ and angle CBO=54∘CBO = 54^\circ. PQPQ is…
  38. 38一个正三棱锥的底面边长为66，侧棱长为15 \sqrt {15}，那么这个正三棱锥的体积是 ___ ．
  39. 39An aircraft waiting to land is flying around a triangular circuit ABC. A, B and C are vertically above three beacons, X,…
  40. 40P, Q, R and S are four villages located on an island, where Q is due north of R. PQ = 924 m, QR = 640 m, PR = 1124 m, RS…
  41. 41The diagram shows four points P, Q, R and S on level ground. Q is due east of P. Angle SPQ = 40° and angle PSR = 15°. PQ…
  42. 42O is the centre of the equilateral triangle. The triangle ABC forms the base of a pyramid. The vertex, X is vertically a…
  43. 43A, B, C, D and E are points on the circle, centre O. QP and QR are tangents to the circle at B and E respectively. AC in…
  44. 44用边长相同的正三角形、正方形、正六边形、正八边形、正十边形进行密铺，每个交叉点只允许五块进行密铺，它有 种铺法．
  45. 45A parallelogram ABCD is drawn on a square grid inside a box. By joining dots on the grid with straight lines, draw squar…
  46. 46In the diagram, BDK is a straight line and AB = AD. Angle ABD = 36°, angle CBD = 49° and angle CDK = 121°. Explain why i…
  47. 47在等边三角形、正五边形、正六边形、正七边形中，既是轴对称又是中心对称的图形是（ ） A. 等边三角形 B. 正五边形 C. 正六边形 D. 正七边形
  48. 48下面图形中是轴对称图形不是中心对称图形的是（ ） A. 正方形 B. 正六边形 C. 圆 D. 正五边形
  49. 49The diagram shows a lecture theatre in the shape of a prism with height 9 metres. The floor of the lecture theatre, ABCD…
  50. 50In the diagram, BP is parallel to CQ. AB = AC = CD, ∠ABP = 19° and ∠QCD = 68°. Calculate ∠CDA. Show workings clearly and…
  51. 51The diagram below shows three points, A, B and C on flat ground. AB = 80 m, AC = 100 m and BC = 90 m. C is due east of A…
  52. 52In the diagram, A, B C and D lie on a circle, centre O. PQ and PR are tangents to the circle at A and D respectively. It…
  53. 53长方形有 ___ 条对称轴，正五边形有 ___ 条对称轴，圆有 ___ 条对称轴．
  54. 54等腰梯形的腰与中位线都是6厘米，则它的周长是 厘米．
  55. 55In the diagram, OBC is the sector of a circle, centre O, and angle BOC = 60∘60^\circ. A and D are the midpoints of OB and…
  56. 56The diagram shows a triangle ABC with AB produced to D. AB=18 cmAB = 18\,\mathrm{cm}, BC=20 cmBC = 20\,\mathrm{cm}, AC=22 cmAC = 22\,\mathrm{cm}…
  57. 57In the diagram, AC is a diameter of the circle ABCD. AB and DC are produced to meet at E. Angle AED = 20° and angle CAD…
  58. 58The diagram shows part of three regular polygons A, B and C fit together at a common vertex. Polygon A is an icosagon, a…
  59. 59In the diagram below, ABCD is a rhombus and the diagonal AC intersects the y-axis at E. Show that triangle AEB is congru…
  60. 60It is given that AB→=(−12a)\overrightarrow{AB}=\begin{pmatrix}-12\\a\end{pmatrix}, a>0a>0 and ∣BA→∣=37|\overrightarrow{BA}|=37 units. F…