triangle geometry - centres of triangle, congruence and similarity of triangles - One Line Questions

1. If ∆ABC ≅ ∆DEF, then ∠B = ∠? — ∠E
2. If ∆ABC ≅ ∆DEF, then the ratio of their perimeters is: — 1:1
3. The medians of a triangle intersect at a point that divides each median in the ratio: — 2:1
4. In ∆ABC, AD is the median to side BC. The centroid G divides AD in the ratio: — 2:1
5. 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: — 1:4
6. If the ratio of corresponding altitudes of two similar triangles is 3:5, then the ratio of their areas is: — 9:25
7. If ∆ABC ~ ∆XYZ, and AB = 2, BC = 3, AC = 4, and XY = 4, then YZ is: — 6
8. The locus of points equidistant from two intersecting lines is: — The angle bisector
9. If triangle ABC is congruent to triangle PQR (denoted as ∆ABC ≅ ∆PQR), then which of the following is true? — AB = PQ
10. If triangle ABC is similar to triangle PQR (denoted as ∆ABC ~ ∆PQR), then which of the following is true? — AB/PQ = BC/QR = AC/PR
11. If two triangles are similar, the ratio of their corresponding sides is equal to the ratio of their: — Perimeters
12. In ∆ABC, if ∠A = 90°, where is the orthocenter located? — At A
13. In ∆ABC, if AB = AC and AD is the altitude to BC, then D is the: — Midpoint of BC
14. The center of the circle passing through the midpoints of the sides of a triangle is the: — Circumcenter of the medial triangle
15. If ∆ABC is equilateral, which of the following points coincide? — All four centers (Centroid, Orthocenter, Circumcenter, Incenter)
16. What is the point of intersection of the medians of a triangle called? — Centroid
17. Which point is equidistant from the sides of a triangle? — Incenter
18. The point of intersection of the angle bisectors of a triangle is called the: — Incenter
19. What is the point of intersection of the perpendicular bisectors of the sides of a triangle called? — Circumcenter
20. Which point is equidistant from the vertices of a triangle? — Circumcenter
21. The point of intersection of the altitudes of a triangle is called the: — Orthocenter
22. The point of concurrency of the angle bisectors is called the: — Incenter
23. The orthocenter, centroid, and circumcenter of a non-equilateral triangle are always: — Collinear
24. Two triangles are similar if their corresponding sides are in the same ratio. This is the property of: — Similarity
25. In ∆ABC, if ∠A = 30°, ∠B = 60°, and ∠C = 90°, and ∆DEF has ∠D = 30°, ∠E = 60°, ∠F = 90°, then the triangles are: — Similar
26. The ratio of the areas of two similar triangles is equal to the square of the ratio of their: — All of the above
27. The point where the perpendicular bisectors of the sides of a triangle meet is called the: — Circumcenter
28. Which center of a triangle is equidistant from the vertices? — Circumcenter
29. The circumcenter of a triangle is the center of its: — Circumscribed circle
30. In an isosceles triangle, the altitude from the vertex angle is also the: — Median and angle bisector
31. In an acute-angled triangle, the orthocenter lies: — Inside the triangle
32. In an obtuse-angled triangle, the orthocenter lies: — Outside the triangle
33. If two triangles are similar, then the ratio of the square of their corresponding altitudes is equal to the ratio of their: — Areas
34. 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? — Basic Proportionality Theorem (Thales' Theorem)
35. In triangle ABC, the angle bisector of ∠A, the median to BC, and the altitude to BC are concurrent if the triangle is: — Isosceles
36. Which congruence criterion requires two angles and a non-included side to be equal? — AAS
37. Which of the following is NOT a criterion for congruence of triangles? — AAA (Angle-Angle-Angle)
38. Which of the following is a criterion for similarity of triangles? — All of the above
39. In a right-angled triangle, the orthocenter is located at: — The vertex of the right angle
40. Which of the following is true for any triangle? — The centroid always lies inside the triangle.
41. Two triangles are said to be congruent if: — They have the same shape and same size
42. Two triangles are said to be similar if: — Their corresponding angles are equal and their corresponding sides are proportional.
43. The AAS congruence rule states that two triangles are congruent if: — Two angles and a non-included side of one triangle are equal to the corresponding angles and side of the other triangle.
44. The SSS congruence rule states that two triangles are congruent if: — All three sides of one triangle are equal to the corresponding sides of the other triangle.
45. The SAS congruence rule states that two triangles are congruent if: — Two sides and the included angle of one triangle are equal to the corresponding sides and angle of the other triangle.
46. The ASA congruence rule states that two triangles are congruent if: — Two angles and the included side of one triangle are equal to the corresponding angles and side of the other triangle.
47. The SSS similarity rule states that two triangles are similar if: — All three sides of one triangle are proportional to the corresponding sides of the other triangle.
48. The SAS similarity rule states that two triangles are similar if: — Two sides of one triangle are proportional to the corresponding sides of the other triangle, and the included angles are equal.
49. The AAA similarity rule states that two triangles are similar if: — All three angles of one triangle are equal to the corresponding angles of the other triangle.
50. If two triangles have the same area, are they necessarily congruent? — No
All One Line Questions
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