TRIANGLES (CDS)

Total Questions: 69

11. In the figure given below, ABC is an equilateral triangle with each side of length 30 cm. XY is parallel to BC. XP is parallel to AC and YQ is parallel to AC and YQ is parallel to AB. If XY + XP + YQ is 40 cm, then the value of PQ is [2018 (II) Evening Shift]

Correct Answer: (d) 10 cm
Solution:Given, AB = BC = AC = 30, XY is parallel to BC

12. In a triangle ABC, the sides AB, AC are produced and the bisectors of exterior angles of ∠ABC and ∠ACB intersect at D. If ∠BAC = 50º, then ∠BDC is equal to [2018 (II) Evening Shift]

Correct Answer: (b) 65º
Solution:∠BDC = 180° - (u + v)


13. If ABC is a right-angled triangle with AC as its hypotenuse, then which one of the following is correct? [2018 (II) Evening Shift]

Correct Answer: (b) AC³ > AB³ + BC³
Solution:Here, ABC is a right angle triangle with AC as its hypotenuse

14. In the figure given below, ∆ABR ~ ∆PQR. If PQ = 3 cm, AB = 6 cm, BR = 8.2 cm and PR = 5.2 cm, then QR and AR are respectively [2018 (II) Evening Shift]

Correct Answer: (d) 4.1 cm, 10.4 cm
Solution:Given, PQ = 3 cm, AB = 6 cm,


15. In the figure given below ABC is a triangle with AB perpendicular to BC. Further BD is perpendicular to AC. If AD = 9 cm and DC = 4cm, then what is the length of BD? [2018 (II) Evening Shift]

Correct Answer: (d) 6 cm
Solution:In ∆ABD,

16. ABC is a triangle right angled at C with BC a = and AC b = . If p is the length of the perpendicular from C on AB, then which one of the following is correct? [2018 (I) Morning Shift]

Correct Answer: (a)
Solution:According to the question,


17. Consider the following statements [2018 (I) Morning Shift]

1. The orthocentre of a triangle always lies inside the triangle.
2. The centroid of a triangle always lies inside the triangle.
3. The orthocentre of a right angled triangle lies on the triangle.
4. The centroid of a right angled triangle lies on the triangle.

Which of the above statements are correct?

Correct Answer: (c) 2 and 3
Solution:2 and 3

18. Consider the following statements Two triangles are said to be congruent, if [2018 (I) Morning Shift]

1. Three angles of one triangle are equal to the corresponding three angles of the other triangle.
2. Three sides of one triangle are equal to the corresponding three sides of the other triangle.
3. Two sides and the included angle of one triangle are equal to the corresponding two sides and the included angle of the other triangle.
4. Two angles and the included side of one triangle are equal to the corresponding two angles and the included side of the other triangle.

Which of the above statements are correct?

Correct Answer: (d) 2, 3 and 4
Solution:2, 3 and 4 are correct.

19. (Questions 19 and 20) Consider the following for the next two (02) questions [2018 (I) Morning Shift]

In a triangle ABC, a b, and c are the lengths of the sides and p q, and r are the lengths of its medians.

Which one of the following is correct?

Correct Answer: (c) 2 (p + q + r) < 3(a + b + c)
Solution:Let AB = c , BC = a, CA = b, AD = p, BE = q, CE = r


20. Which one of the following is correct [2018 (I) Morning Shift]

Correct Answer: (b) 3(a + b + c) < 4(p + q + r)
Solution: