Math topic中文

Solving problems

solving simple problems involving similarity and congruence

Practice questions

  1. 1A cuboid has a volume of 250 cm^3, correct to the nearest cubic centimetre. The height of the cuboid is 8.4 cm, correct…
  2. 2In 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…
  3. 3In 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…
  4. 4高22米的旗杆在水平地面上的影长为33米，此时测得附近一个建筑物的影长1212米，则该建筑物的高度为()(\quad) A. 18                          18\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: …
  5. 5Figure 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…
  6. 6CBEO is a parallelogram. The position vectors of C and E, relative to O, are a\mathbf{a} and b\mathbf{b} respectively.…
  7. 7In the diagram, ABC is an equilateral triangle, ACDE is a square and angle FAC = 15°. Show that triangle EAF and triangl…
  8. 8The diagram shows a circle and a chord AB. B is due east of A. Locate and label a point C on the circle such that ∠ABC=110∘\angle ABC = 110^\circ…
  9. 9On the map, 3 MRT stations, Braddell (NS18), Caldecott (CC17) and Toa Payoh (NS19) are joined to form a triangle. constr…
  10. 10In the diagram, ABC and ACD are triangles such that angle ACB = angle ADC. Show that the two triangles are similar. Answ…
  11. 11Construct triangle ABC where AC is 10 cm and angle BAC = 40°. AB has already been drawn. Construct the perpendicular bis…
  12. 12The diagram represents a plot of land, ABCD. The police is looking for a robber hiding in the land. Scale: 1 cm represen…
  13. 13A manufacturer sells drinks in bottles of two sizes that are geometrically similar. Some specifications for the bottles…
  14. 14In 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…
  15. 15A, B, C and D are points on horizontal ground. AB = 35 m and BC = 68 m. The bearing of B from A is 137∘137^\circ and the b…
  16. 16Two empty paper cups are geometrically similar. The thickness of the paper used is negligible. The big cup can be filled…
  17. 17The diagram shows five towns A, B, C, D and E. Towns B, C, D lie on a straight line. Town E is due east of Town D. It is…
  18. 18In 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…
  19. 19In the diagram below, triangle ABC is congruent to triangle PNA. Given that BC = 22 cm, AP = 32 cm and angle ACB = 91°,…
  20. 20In the diagram, ABC and AED are straight lines and BE is parallel to CD. Show that triangle ABE is similar to triangle A…
  21. 21The figure shows a triangle ABC. E is the mid-point of AC. AB‾=3a\overline{AB}=3a and AC‾=3c\overline{AC}=3c. K lies on EB such…
  22. 22The 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…
  23. 23ABCD 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…
  24. 24A 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…
  25. 25张亮同学想利用树影测量校园内的树高，他在某一时刻测得小树高为1.6米时，其影长为0.8米，当他测量教学楼旁的一棵大树影长时，因大树靠近教学楼，有一部分影子在墙上．经测量，地面部分影长为4.8米，墙上影长为1.2米，那么这棵大树高约 米．
  26. 26The diagram represents a plot of land, EFGH, which is to be used for an observatory. Construct the bisector of the angle…