triangle geometry - centres of triangle, congruence and similarity of triangles - Question Bank
1. The orthocenter, centroid, and circumcenter of a non-equilateral triangle are always:
2. If ∆ABC ~ ∆DEF, and the ratio of similarity is 1:2, then the ratio of the area of ∆ABC to the area of ∆DEF is:
3. Which theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio?
4. The point of concurrency of the angle bisectors is called the:
5. If two triangles are similar, then the ratio of the square of their corresponding altitudes is equal to the ratio of their:
6. In triangle ABC, the angle bisector of ∠A, the median to BC, and the altitude to BC are concurrent if the triangle is:
7. If the ratio of corresponding altitudes of two similar triangles is 3:5, then the ratio of their areas is:
8. The center of the circle passing through the midpoints of the sides of a triangle is the:
9. In ∆ABC, if ∠A = 30°, ∠B = 60°, and ∠C = 90°, and ∆DEF has ∠D = 30°, ∠E = 60°, ∠F = 90°, then the triangles are:
10. If ∆ABC ≅ ∆DEF, then the ratio of their perimeters is:
11. Which of the following is true for any triangle?
12. Two triangles are similar if their corresponding sides are in the same ratio. This is the property of:
13. If ∆ABC is equilateral, which of the following points coincide?
14. In ∆ABC, if AB = AC and AD is the altitude to BC, then D is the:
15. If two triangles have the same area, are they necessarily congruent?
16. In an isosceles triangle, the altitude from the vertex angle is also the:
17. The locus of points equidistant from two intersecting lines is:
18. If ∆ABC ~ ∆XYZ, and AB = 2, BC = 3, AC = 4, and XY = 4, then YZ is:
19. Which congruence criterion requires two angles and a non-included side to be equal?
20. If ∆ABC ≅ ∆DEF, then ∠B = ∠?
21. In ∆ABC, if ∠A = 90°, where is the orthocenter located?
22. Which center of a triangle is equidistant from the vertices?
23. The point where the perpendicular bisectors of the sides of a triangle meet is called the:
24. In ∆ABC, AD is the median to side BC. The centroid G divides AD in the ratio:
25. The ratio of the areas of two similar triangles is equal to the square of the ratio of their:
26. If two triangles are similar, the ratio of their corresponding sides is equal to the ratio of their:
27. The AAA similarity rule states that two triangles are similar if:
28. The SAS similarity rule states that two triangles are similar if:
29. The SSS similarity rule states that two triangles are similar if:
30. If triangle ABC is similar to triangle PQR (denoted as ∆ABC ~ ∆PQR), then which of the following is true?
31. Which of the following is a criterion for similarity of triangles?
32. Two triangles are said to be similar if:
33. The AAS congruence rule states that two triangles are congruent if:
34. The ASA congruence rule states that two triangles are congruent if:
35. The SAS congruence rule states that two triangles are congruent if:
36. The SSS congruence rule states that two triangles are congruent if:
37. If triangle ABC is congruent to triangle PQR (denoted as ∆ABC ≅ ∆PQR), then which of the following is true?
38. Which of the following is NOT a criterion for congruence of triangles?
39. Two triangles are said to be congruent if:
40. In a right-angled triangle, the orthocenter is located at:
41. In an obtuse-angled triangle, the orthocenter lies:
42. In an acute-angled triangle, the orthocenter lies:
43. The point of intersection of the altitudes of a triangle is called the:
44. Which point is equidistant from the vertices of a triangle?
45. The circumcenter of a triangle is the center of its:
46. What is the point of intersection of the perpendicular bisectors of the sides of a triangle called?
47. The point of intersection of the angle bisectors of a triangle is called the:
48. Which point is equidistant from the sides of a triangle?
49. The medians of a triangle intersect at a point that divides each median in the ratio:
50. What is the point of intersection of the medians of a triangle called?