Math topic中文

Parallel transversal

angles formed by two parallel lines and a transversal: corresponding angles, alternate angles, interior angles

Practice questions

  1. 1已知四边形ABCD，从下列条件中：（1）AB∥CD；（2）BC∥AD；（3）AB=CD；（4）BC=AD；（5）∠A=∠C；（6）∠B=∠D．任取其中两个，可以得出“四边形ABCD是平行四边形”这一结论的情况有（ ） A. 4种 B. 9种…
  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. 3如图，给出了过直线外一点作已知直线的平行线的方法，其依据是（ ）。 A. 同位角相等，两直线平行 B. 内错角相等，两直线平行 C. 同旁内角互补，两直线平行 D. 两直线平行，同位角相等
  4. 4In 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…
  5. 5In the diagram ABCDE is a regular pentagon. BE and BD are straight lines. Find, giving reasons for each answer, angle AB…
  6. 6The diagram shows a parallelogram ABCD on horizontal ground where AC is a path. AB = 15 m and BC = 8 m. The bearing of B…
  7. 7The 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…
  8. 8下列语句中，不是真命题的是（ ） A. 两个锐角的和是钝角 B. 直角的补角是直角 C. 对顶角相等 D. 两直线平行，同位角相等
  9. 9The 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…
  10. 10下列命题中，是真命题的是()(\quad) A. 内错角相等 B. 对顶角相等 C. 若x2=4x^{2}=4，则x=2x=2 D. 若a>ba>b，则a2>b2a^{2}>b^{2}
  11. 11In the figure below, AB, CD, WX and YZ are straight lines. Which one of the following statements is correct?
  12. 12The angles of a quadrilateral taken in order are 3xx, 6xx, 5xx and 4xx. Find the value of xx. Answer xx = ___ Expl…
  13. 13下列命题是假命题的是()(\quad) A. 对顶角相等 B. 两直线平行，同位角相等 C. 内错角相等，两直线平行 D. 三角形的外角大于内角
  14. 14PQRS are points on the circumference of a circle, centre O. Angle OQR = 50°, angle PSR = 73° and obtuse angle SOQ = 156°…
  15. 15两条直线被第三条直线所截，如果内错角相等，则同旁内角 ．
  16. 16The diagram shows a rectangular table ABCD arranged such that the side AD is inclined at an angle of θ\theta to the wal…
  17. 17“两直线平行，内错角相等”的逆命题是___．
  18. 18如图，AB∥CD，点E在BC上，∠BED＝68°，∠D＝38°，则 ∠B的度数为（ ） A. 30° B. 34° C. 38° D. 68°
  19. 19A, 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…
  20. 20In the diagram, OAB is a sector of a circle with centre O. Given that OA = 12 cm, ∠AOB = θ\theta radians, OC = 8 cm and…
  21. 21下列正确说法的个数是( ) ①① 同位角相等 ②② 对顶角相等 ③③ 等角的补角相等 ④④ 两直线平行，同旁内角相等 A. 11 B. 22 C. 33 D. 44
  22. 22In the diagram, BP is parallel to CQ. AB = AC = CD, ∠ABP = 19° and ∠QCD = 68°. Calculate ∠CDA. Show workings clearly and…
  23. 23In 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…
  24. 24A, 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…
  25. 25下列说法正确的是( ) Ａ．内错角相等 Ｂ．任何数的0次方都等于1 Ｃ．一个角的补角一定大于它本身 Ｄ．平行于同一直线的两条直线互相平行
  26. 26ABCD is a rhombus and RD = CS. SCB, DCR and AQR are straight lines. Prove that triangles SCD and RDA are congruent.
  27. 27In the pentagon ABCDE shown, angle BAE = 60° and angle BCD = 45°. AE is parallel to CD, E lies on CB extended and CE = D…
  28. 28In the diagram, two circles with centres O and P respectively intersects at A. The two circles have the same radius and…
  29. 29The diagram shows a rhombus ABCD. ABQ, PBC and DRQ are straight lines and AQ = BP. State the triangle that is similar to…
  30. 30若∠AOC=42∘∠AOC=42^{\circ}，O′A′/ ⁣/OAO′A′/\!/OA，O′C′=OCO′C′=OC，且∠A′O′C′∠A′O′C′为钝角，则∠A′O′C′=∠A′O′C′=___．
  31. 31The figure is made up of a 7-sided regular polygon with centre O, a triangle OAG and a parallelogram OHFG, where GF is p…
  32. 32若两条平行直线被第三条直线所截，则()() A. 一对同旁内角的角平分线互相垂直 B. 一对内错角的角平分线互相垂直 C. 一对同位角的角平分线互相垂直 D. 以上都不对
  33. 33下列说法正确的个数是（ ） ①同一平面内两条不相交的直线一定平行 ； ②垂直于同一直线的两条直线平行；③若直线AB∥CD，AE∥CD,则AB与AE一定重合； ④同位角相等. A. 1个 B. 2个 C. 3个 D. 4个
  34. 34A, 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…
  35. 35In the figure, a rectangular piece of paper is folded twice. ∠GDA=36∘\angle GDA = 36^\circ and ∠ADE=10∘\angle ADE = 10^\circ. Find ∠DAF\angle DAF…
  36. 36In the figure below, ACE is a triangle, BDEF is a parallelogram, BFG is an isosceles triangle and AE parallel to BD. Fin…
  37. 37ABCD is a parallelogram and triangle CDE is isosceles. E and F are points on AD and BC respectively. AB, EF and CD are p…
  38. 38The figure below is made up of a trapezium and 2 parallel lines. Study the figure and answer the following questions. wh…
  39. 39平行线的判别： 角相等， 角相等， 角互补，两直线平行．
  40. 40In the diagram, ABC and AED are straight lines and BE is parallel to CD. Show that triangle ABE is similar to triangle A…
  41. 41下列命题：①平面内，垂直于同一条直线的两直线平行；②经过直线外一点，有且只有一条直线与这条直线平行；③垂线段最短；④同旁内角互补.其中，正确命题的个数有()(\quad) A. 33个 B. 22个 C. 11个 D.…
  42. 42In the diagram below, PQRST is a trapezium made up of a parallelogram PQRS and an isosceles triangle PST where PT = PS.…
  43. 43A regular m-sided polygon and a regular n-sided polygon are joined together. Part of the polygons are shown below. ∠BCD:∠DCG=5:3\angle BCD : \angle DCG = 5 : 3…
  44. 44在梯形ABCD中，AD∥BC，AB=DC=3，沿对角线BD翻折梯形ABCD，若点A恰好落在下底BC的中点E处，则梯形的周长为 。
  45. 45The diagram shows triangle ABC and parallelogram BDEF. FE bisects angle DEC and angle FEC = x∘x^\circ. Find angle ECF in…
  46. 46In the figure, circle ABCF and circle CDEF intersect at C and F. AFD and BFE are straight lines and BC is parallel to AD…
  47. 47ABCD 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…
  48. 48下列命题是真命题的有___.(.(填序号)①)①对顶角相等；②②两直线平行，内错角相等；③③两个锐角对应相等的两个直角三角形全等；④④点P(1,2)P(1,2)关于xx轴的对称点的坐标是(−1,−2)(-1,-2)．
  49. 49下列命题：①①同位角相等； ②②内错角相等； ③③对顶角相等；④④邻补角互补；⑤⑤同旁内角互补，其中真命题的个数为()() A. 22个 B. 33个 C. 44个 D. 55个
  50. 50In the diagram, A, B, C and D are points on the circumference of a circle with centre O. AB is parallel to DO and ∠AOD=67∘\angle AOD = 67^\circ…
  51. 51The diagram shows a rhombus ABCD. ABQ, PBC and DRQ are straight lines and AQ = BP. State the triangle that is similar to…
  52. 52平行四边形的两个邻角的和是（ ） A. 180° B. 360° C. 90°
  53. 53The diagram shows a triangle AGD with the points C and B lying on AD and points E and F lying on GD. It is given that CE//BF//AGCE//BF//AG…
  54. 54OACB is a quadrilateral. OB is parallel to AC. D is the point on BC such that BD=13BCBD = \frac{1}{3} BC. The lines OB and AD…
  55. 55已知两个角的两边分别平行，且这两个角的度数分别为(2x−10)°(2x-10)°和(110−x)°(110-x)°，则x=x=___.
  56. 56四边形ABCD各角的比为∠A：∠B：∠C：∠D=1：2：3：4，则这个四边形为 ．
  57. 57两条不平行的直线被第三条直线所截,下列说法可能成立的是（ ） A. 同位角 相等 B. 内错角相等 C. 同旁内角相等 D. 同旁内角互补
  58. 58In the diagram, P, Q, R, S and T are points on the circle with centre O. VX is a tangent to the circle at P. Line SR is…
  59. 59下列四个命题：①对顶角相等；②内错角相等；③平行于同一条直线的两条直线互相平行；④如果一个角的两边分别平行于另一个角的两边，那么这两个角相等．其中真命题的个数是（ ） A. 1个 B. 2个 C. 3个 D. 4个