Math topic中文

Determining triangles

determining whether two triangles are

  • congruent
  • similar

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. 2下列条件中能判定△ABC≌△DEF的是（ ） A. AB=DE，BC=EF，∠A=∠D B. ∠A=∠D，∠B=∠E，∠C=∠F C. AC=DF，AB=DE D. ∠B=∠E，∠C=∠F，AC=DF
  3. 3A, 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…
  4. 4下列说法正确的是 ①有两条边对应相等的两个直角三角形全等； ②斜边对应相等的两个等腰直角三角形全等； ③有一条直角边对应相等的两个等腰三角形全等； ④一锐角和一边对应相等的两个直角三角形全等．
  5. 5In 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…
  6. 6The diagram below shows part of a regular 18-sided polygon, ABCDEF... The lines BC and ED are extended to meet at the po…
  7. 7ABCD is a square and AQ is perpendicular to PR. PQR and ADR are straight lines. DQ : DC = 1 : 2. Show that triangle DQR…
  8. 8The 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…
  9. 9In the diagram, ABCD is a rectangle. OAB is a sector of a circle, centre O. OXD and OYC are straight lines. Show that tr…
  10. 10In the diagram, ABC is an equilateral triangle, ACDE is a square and angle FAC = 15°. Show that triangle EAF and triangl…
  11. 11The equation of the line l1l_1 is x+4y=20x + 4y = 20. The line cuts the x-axis at point A and the y-axis at point B. Another…
  12. 12在 Rt△ ABC{\rm Rt}\triangle\:ABC和 Rt△ DEF{\rm Rt}\triangle\:DEF中， AB= DEAB=\:DE，∠ A=∠ D=90°∠\:A=∠\:D=90°，再补充一个条件 ，便可得 Rt△ ABC≌ Rt△ DEF.{\rm Rt}\triangle\:ABC≌\:{\rm Rt}\triangle\:DEF. …
  13. 13In the diagram, ABC and ACD are triangles such that angle ACB = angle ADC. Show that the two triangles are similar. Answ…
  14. 14PR is a diameter of the large circle, centre O. QS is a diameter of the small circle, centre O. PQ and RS are tangents t…
  15. 15下列说法中： ①如果两个三角形可以依据“AAS”来判定全等，那么一定也可以依据“ASA”来判定它们全等； ②如果两个三角形都和第三个三角形不全等，那么这两个三角形也一定不全等； ③要判断两个三角形全等，给出的条件中至少要有一对边对应相等．…
  16. 16In 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…
  17. 17A, B and C are points on the circle centre O and AB = BC. P is the midpoint of chord AB and Q is the midpoint of chord B…
  18. 18In the diagram below, ABCD is a rhombus and the diagonal AC intersects the y-axis at E. Show that triangle AEB is congru…
  19. 19下列说法中正确的是()() A. 斜边相等的两个直角三角形全等 B. 腰相等的两个等腰三角形全等 C. 有一边相等的两个等边三角形全等 D. 两条边相等的两个直角三角形全等
  20. 20根据下列条件不能唯一画出△ABC\triangle ABC的是()(\quad) A. AB=5AB=5，BC=6BC=6，AC=7AC=7 B. AB=5AB=5，BC=6BC=6，∠B=45°∠B=45° C. AB=5AB=5，AC=4AC=4…
  21. 21ABCD is a rhombus and RD = CS. SCB, DCR and AQR are straight lines. Prove that triangles SCD and RDA are congruent.
  22. 22In the diagram, O is the centre of two concentric circles. X and Y lie on the circumference of the smaller circle, while…
  23. 23In 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…
  24. 24In the diagram, two circles with centres O and P respectively intersects at A. The two circles have the same radius and…
  25. 25下列命题中正确的命题是（ ） A. 有两条边及其中一边的对角对应相等的两个三角形全等 B. 两个等边三角形全等 C. 各有一个角是40°的两个等腰三角形全等 D. 三条边对应相等的两个三角形的对应角也相等
  26. 26ABCD 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…
  27. 27The diagram shows a rhombus ABCD. ABQ, PBC and DRQ are straight lines and AQ = BP. State the triangle that is similar to…
  28. 28将点A（3，1）绕原点O顺时针旋转90°到点B，则点B的坐标是 ．
  29. 29下列说法：①有两条直角边对应相等的两个直角三角形全等；②有斜边对应相等的两个等腰直角三角形全等；③有一条直角边和斜边上的高对应相等的两个直角三角形全等；④有一条边相等的两个等腰直角三角形全等．其中正确的有（ ） A. 1个 B. 2个 C.…
  30. 30下列说法错误的是()() A. 三角形中至少有两个锐角 B. 两条边及一角对应相等的三角形全等 C. 两个角及一边对应相等的三角形全等 D. 三角形的外角大于不相邻的内角
  31. 31写出下列命题的“若p，则q”形式，并写出它的逆命题、否命题与逆否命题，并判断它们的真假． （1）全等三角形的对应边相等； （2）四条边相等的四边形是正方形．
  32. 32In 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…
  33. 33下列命题中，是真命题的是（ ） A. 有两边和其中一边的对角对应相等的两个三角形全等 B. 等腰三角形既是轴对称图形，也是中心对称图形 C. 轴对称图形的对称轴是连接两个对称点之间的线段的垂直平分线 D. 任何数的零次幂都等于1
  34. 34The diagram shows two concentric circles with centre O. PQ is the diameter of the larger circle and RS is the diameter o…
  35. 35In 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…
  36. 36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 ．
  37. 37The diagram, not drawn to scale, shows two concentric circles, centre O. AB and AD are tangents to the smaller circle at…
  38. 38Triangle ABC is equilateral. CAD and ABE are straight lines and AD = BE. Show that triangle ABD and triangle BCE are con…
  39. 39In the diagram, AB = DC and AC = DB. The line BD intersect the line AC at T. Prove that △ABC\triangle ABC is congruent to…
  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. 41In the diagram below, PQRST is a trapezium made up of a parallelogram PQRS and an isosceles triangle PST where PT = PS.…
  42. 42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…
  43. 43如果四边形ABCD的对角线相交于点O，且AO=CO，那么下列条件中不能判断四边形ABCD为平行四边形的是（ ） A. OB=OD B. AB∥CD C. AB=CD D. ∠ADB=∠DBC
  44. 44A, B and C are points on the circumference of a circle. Angle CAB = angle CBA. DA and DB are tangents to the circle from…
  45. 45The 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…
  46. 46下列命题是真命题的是 ． ①一个锐角及这个锐角的对边对应相等的两个直角三角形全等． ②有两边对应相等的两个直角三角形全等． ③有两边及一角对应相等的两个三角形全等． ④有两锐角及一边对应相等的两个三角形全等．
  47. 47The diagram shows triangle ABC and parallelogram BDEF. FE bisects angle DEC and angle FEC = x∘x^\circ. Find angle ECF in…
  48. 48In the figure, circle ABCF and circle CDEF intersect at C and F. AFD and BFE are straight lines and BC is parallel to AD…
  49. 49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)．
  50. 50The diagram shows a parallelogram ABCD. APQ, BRQ, CRS and DPS are straight lines which bisect angles A, B, C and D respe…
  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下列各组所述几何图形中，一定全等的是()(\quad) A. 一个角是45°45°的两个等腰三角形 B. 腰长相等的两个等腰直角三角形 C. 两个等边三角形 D. 各有一个角是40°40°，腰长都是8cm8cm的两个等腰三角形
  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下列条件不能证明两个直角三角形全等的是()(\quad) A. 斜边和一直角边对应相等 B. 一直角边和一角对应相等 C. 两条直角边对应相等 D. 斜边和一锐角对应相等
  56. 56在△ABC\triangle ABC 中， ADAD 是中线，BC=12BC=12 ，∠B=∠DAC∠B=∠DAC ，则线段 ACAC 的长为()() A. 44 B. 626 \sqrt{2} C. 66 D. 636 \sqrt{3} …
  57. 57The diagram shows a square ABCD. The diagonals of the square intersect at W and X is a point on the diagonal BD. Y lies…
  58. 58根据下列已知条件，能惟一画出△ABC的是（ ） A. AB=3，BC=4，CA=8 B. ∠A=60°，∠B=45°，AB=4 C. AB=4，BC=3，∠A=30° D. ∠C=90°，AB=6