Math topic中文

Properties similar

properties of similar triangles and polygons:

  • corresponding angles are equal
  • corresponding sides are proportional

Practice questions

  1. 1In the diagram, there are two right-angled triangles ΔABD and ΔCEB such that AD = 12 cm, BD = 15 cm and BE = 20 cm. Find…
  2. 2A cuboid has a volume of 250 cm^3, correct to the nearest cubic centimetre. The height of the cuboid is 8.4 cm, correct…
  3. 3The points A, B, C, D and E are shown in the diagram below such that ABC and AED are straight lines and BE = 8\sqrt{8}…
  4. 4In the diagram, triangle XYZ is similar to triangle UXS. Given that US=UX=9US = UX = 9 cm, XY=XZ=20XY = XZ = 20 cm and YZ=12YZ = 12 cm…
  5. 5The diagram below shows a gift souvenir formed by joining the plane face of a solid hemisphere of radius 3 cm and a soli…
  6. 6The 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…
  7. 7The figure above shows a solid. The cross-section of the solid is a sector of a circle of radius 5 cm and angle 30°. The…
  8. 8In the diagram, P, Q, R and S are points on a circle. PR and QS meet at T. Show that triangle PTS and triangle QTR are s…
  9. 9在Rt△ABC中，各边的长度都扩大两倍，那么锐角A的各三角函数值（ ） A. 都扩大两倍 B. 都缩小两倍 C. 不变 D. 都扩大四倍
  10. 10Isoceles △ABC\triangle ABC has equal side lengths ABAB and BCBC. In the figure below, segments are drawr parallel to AC‾\overline{AC}…
  11. 11Figure I shows a piece of wood is in the form of a right circular cone with a base diameter of 18 cm. The curved surface…
  12. 12The diagram below shows part of a regular 18-sided polygon, ABCDEF... The lines BC and ED are extended to meet at the po…
  13. 13The diagram shows an inverted hollow paper cone with a base of radius rr cm and a height of hh cm. The cone is filled…
  14. 14已知△ABC∽△A'B'C'，它们的相似比为2：3，那么它们的周长比是（ ） A. 2：3 B. 3：2 C. 4：9 D. 9：4
  15. 15The diagram shows two open containers, a right cylinder and an inverted frustum. The right cylinder has a base radius of…
  16. 16In the diagram, ABCD is a rectangle. OAB is a sector of a circle, centre O. OXD and OYC are straight lines. Show that tr…
  17. 17两个相似三角形相似之比为2：3，周长之差为10cm，则它们的周长分别为 ．
  18. 18两个相似三角形的一对对应边的长分别是35cm和14cm，它们的周长相差60cm，求这两个三角形的周长．
  19. 19In the diagram, ABC and ACD are triangles such that angle ACB = angle ADC. Show that the two triangles are similar. Answ…
  20. 20The diagram below shows two circles, with the same centre at O. Points A, B and C lie on the bigger circle and point D l…
  21. 21The diagram below shows an indoor adventure park in the shape of a trapezoidal prism with a square base ABCD. The indoor…
  22. 22In the diagram, ACD is a triangle. B is the point on AC such that AB = 10 cm and BC = 4 cm. E is the point on AD where A…
  23. 23如果一个角是10°10°，用66倍的放大镜观察，这个角应是___°.°.
  24. 24A closed conical ornament has a circular base of radius 10 cm and height 25 cm, and contains mercury to a depth of 15 cm…
  25. 25The diagram shows two geometrically similar containers. The cost of painting the base area of the smaller container is 2564\frac{25}{64}…
  26. 26△ABC\triangle ABC与△A′B′C′\triangle A′B′C′是位似图形，且△ABC\triangle ABC与△A′B′C′\triangle A′B′C′的位似比是11：22，已知△ABC\triangle ABC的…
  27. 27Two empty paper cups are geometrically similar. The thickness of the paper used is negligible. The big cup can be filled…
  28. 28已知△ABC∽△DEF且对应中线之比为9：16，则△ABC与△DEF的周长之比为（ ） A. 4：3 B. 3：4 C. 16：9 D. 9：16
  29. 29In the diagram, ABAB is the diameter of the circle. AED and ABC are straight lines. AE=12AE = 12 cm and EB=16EB = 16 cm. ∠ADC\angle ADC…
  30. 30Three tin containers are geometrically similar. The heights of tin container A and tin container C are 8 cm and 16 cm re…
  31. 31A container is a prism with a cross section in the shape of a right-angled triangle. The container has a height of 12 cm…
  32. 32ABCD is a trapezium. F is a point on CD such that ABCF is a rhombus and 3AE=2EF3AE = 2EF. Show that triangles ABE and FDE are…
  33. 33The following diagram shows 2 geometrically similar boxes of cereals of the same brand. Show that the cost of the cereal…
  34. 34The diagram shows a rhombus ABCD. ABQ, PBC and DRQ are straight lines and AQ = BP. State the triangle that is similar to…
  35. 35已知△ABC∽△DEF，且周长之比为1：9，则△ABC与△DEF的高的比为（ ） A. 1：3 B. 1：9 C. 1：18 D. 1：81
  36. 36In the diagram, ABTC is a cyclic quadrilateral. QTP is a tangent to the circle and ∠BAT=2∠CAT\angle BAT = 2\angle CAT. The lines…
  37. 37In the diagram, O is the centre of the circle through A, B, C, D and TB is the tangent at B. AC is the diameter of the c…
  38. 38在△ABC中，AB=3，AC=4，△ABC绕着点A旋转后能与△AB′C′重合，那么△ABB′与△ACC′的周长之比为 ．
  39. 39A, B, C and D are points on a circle. Line PCQ is a tangent to the circle. Line QE bisects angle AEC and is parallel to…
  40. 40A conical container with a diameter of 10 cm and a height of 8 cm is filled with water to a depth of 4 cm. Show that the…
  41. 41Triangle ABC is equilateral. CAD and ABE are straight lines and AD = BE. Show that triangle ABD and triangle BCE are con…
  42. 42The diagram shows two geometrically similar cup and saucer sets. The diameter of the smaller saucer is 5 cm. The diamete…
  43. 43如果一个三角形的三边长分别为55、1212、1313，与其相似的三角形的最长的边为3939，那么较大的三角形的周长为 ___ ．
  44. 44John made a triangular poster for the coming mathematics competition. It was in the shape of an equilateral triangle wit…
  45. 45下列结论中，错误的有：（ ） ①所有的菱形都相似； ②放大镜下的图形与原图形不一定相似； ③等边三角形都相似； ④有一个角为110度的两个等腰三角形； ⑤所有的矩形不一定相似． A. 1个 B. 2个 C. 3个 D. 4个
  46. 46已知两个三角形相似，其中一个三角形的两个角分别为72°、63°，则另一个三角形的最小的内角为（ ） A. 72° B. 63° C. 45° D. 不能确定
  47. 47In the diagram, ABC and AED are straight lines and BE is parallel to CD. Show that triangle ABE is similar to triangle A…
  48. 48A cylinder X has radius, rr cm and height hh cm. A hemisphere S is such that its radius is half of the radius of cylin…
  49. 49在△ABC\triangle ABC与△DEF\triangle DEF中，已知ABDE=BCEF=CAFD=34\dfrac{AB}{DE}=\dfrac{BC}{EF}=\dfrac{CA}{FD}=\dfrac{3}{4}，且△ABC\triangle ABC…
  50. 50A liquid container, 30 cm tall, can be modelled by a frustum, A, placed below a cylinder B, as shown in Figure 1. Figure…
  51. 51A paper cup is in the shape of an inverted cone. The diameter of the top of the cup is 8 cm. The height of the cone is 6…
  52. 52The diagram shows triangle ABD and BCD is a straight line. It is also known that AB=7AB = 7 cm, BC=5BC = 5 cm and ∠BAC=∠ADC\angle BAC = \angle ADC…
  53. 53The diagram shows triangle ABC and parallelogram BDEF. FE bisects angle DEC and angle FEC = x∘x^\circ. Find angle ECF in…
  54. 54The base areas of two geometrically similar cones are in the ratio of 9 : 49. If the volume of the bigger cone is 1200 c…
  55. 55The diagram shows a right pyramid of height 45 cm. The volume of the liquid in the pyramid is half the volume of the pyr…
  56. 56ABCD is a parallelogram and G is a point on BD. The line BF produced meets DC at F and AD produced at E. GF is parallel…
  57. 57A piece of A0-sized paper has a total surface area of 1 m^2. The length and breadth of the A0-sized paper are x m and y…
  58. 58已知一圆锥的母线长为10cm10cm，底面半径为6cm.(1)6cm.(1)求圆锥的高;(2);(2)若圆锥内有一球，球与圆锥的底面及圆锥的所有母线都相切，求球的表面积和体积.
  59. 59The diagram shows a rhombus ABCD. ABQ, PBC and DRQ are straight lines and AQ = BP. State the triangle that is similar to…
  60. 60已知一个三角形的三边长分别为5，8，7，则另一个与之相似的三角形的三边长可以是 ．（任写一组即可）