TRIANGLES (CDS)

Total Questions: 69

31. Which one of he following triples does not represent the sides of a triangle? [2017 (I) Morning Shift]

Correct Answer: (d) (2, 3, 6)
Solution:If, a, b, c represents the sides of the triangle, then sum of the two sides must be greater than the third side. Since, 2 + 3 < 6
∴ (2, 3, 6) can't be side of a triangle.

32. The angles of a triangle are in the ratio 2 : 4 : 3 The smallest angle of the triangle is [2017 (I) Morning Shift]

Correct Answer: (b) 40º
Solution:Since, the angles of a triangle are in the ratio 2 : 4 : 3.

33. ABC is a triangle and D is a point on the side BC. If BC = 12 cm, BD = 9 cm and ∠ADC = ∠BAC, then the length of AC is equal to [2017 (I) Morning Shift]

Correct Answer: (b) 6 cm
Solution:In ∆ABC and ∆DAC,

34. In a trapezium ABCD, AB is parallel to CD and the diagonals intersect each other at O. What is the ratio of OA to OC equal to? [2017 (I) Morning Shift]

Correct Answer: (a) Ratio of OB to OD
Solution:

35. In the figure given below ∠A = 80° and ZABC = 60°. BD and CD bisect angles B and C respectively. What are the values of x and y respectively? [2017 (I) Morning Shift]

Correct Answer: (c) 20 and 130
Solution:We have, ∠A = 80° and ∠ABC = 60°


36. In the figure given below, PQR is a non-isosceles right-angled triangle, right angled at Q. If LM and QT are parallel and QT PT = then what is ∠RLM equal to? [2017 (I) Morning Shift]

Correct Answer: (b) ∠LRM
Solution:


37. In the figure given below, ABC is a triangle with AB BC = and D is an interior point of the triangle ABC such that ∠DAC = ∠DCA. [2017 (I) Morning Shift]

Consider the following statements
1. Triangle ADC is an isosceles triangle.
2. D is the centroid of the triangle ABC.
3. Triangle ABD is congruent to the triangle CBD.

Which of the above statements are correct?

Correct Answer: (c) 1 and 3
Solution:


38. In the figure given below, M is the mid-point of AB and ∠DAB = ∠CBA and ∠AMC = ∠BMD. Then the triangle ADM is cong [2017 (I) Morning Shift]

Correct Answer: (c) ASA rule
Solution:


39. ABCD is a square. X is the mid-point of AB and Y is the mid-point of BC. [2017 (I) Morning Shift]

Consider the following statements
1. Triangles ADX and BAY are congruent
2. ∠DXA = ∠ AYB
3. DX is inclined at an angle 60º with AY
4. DX is not perpendicular to AY

Which of the above statements are correct?

Correct Answer: (d) 1 and 2
Solution:


40. Let ABC be a right angled triangle with BC = 5cm and AC = 12. Let D be a point on the hypotenuse AB such that ∠BCD = 30°. What is length of CD? [2016 (II) Evening Shift]

Correct Answer: (d)
Solution:Given, ∆ACB is a right angled triangle, at C, Where, BC = 5 cm and AC = 12 cm.