NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties MCQ, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties MCQ.
NCERT Solutions for Class 7 Maths Chapter 6 The Triangle and its Properties MCQ
Important Multiple Choice Questions
1. How many elements are there in a triangle?
(a) 3
(b) 6
(c) 4
(d) None of these.
2. How many vertices does a triangle have?
(a) 1
(b) 2
(c) 3
(d) 4.
3. How many sides are there in a triangle?
(a) 1
(b) 2
(c) 3
(d) 4.
4. How many angles are there in a triangle?
(a) 1
(b) 2
(c) 3
(d) 4.
5. If two sides of a triangle are not equal, the triangle is called
(a) scalene
(b) isosceles
(c) equilateral
(d) right-angled.
6. If two sides of a triangle are equal, the triangle is called
(a) isosceles
(b) equilateral
(c) scalene
(d) right-angled.
7. If all the three sides of a triangle are equal, the triangle is called
(a) equilateral
(b) right-angled
(c) isosceles
(d) scalene.
8. If all the angles of a triangle are acute, the triangle is called
(a) obtuse-angled
(b) acute-angled
(c) right-angled
(d) none of these.
9. If one angle of a triangle measures 90°, the triangle is called
(a) acute-angled
(b) obtuse-angled
(c) right-angled
(d) none of these.
10. If one angle of a triangle is obtuse, the triangle is called
(a) acute-angled
(b) obtuse-angled
(c) right-angled
(d) none of these.
11, How many medians can a triangle have?
(a) 1
(b) 2
(c) 3
(d) 4
12. How many altitudes can a triangle have?
(a) 1
(b) 2
(c) 3
(d) 4.
13. The total measure of the three angles of a triangle is
(a) 360°
(b) 90°
(c) 180°
(d) none of these.
14. The measure of each angle of an equilateral triangle is
(a) 30°
(b) 45°
(c) 90°
(d) 60°.
15. Which of the following statements is true?
(a) A triangle can have two right angles
(b) A triangle can have two obtuse angles
(c) A triangle can have two acute angles
(d) A triangle can have all the three angles less than 60°.
16. Which of the following statements is true?
(a) A triangle can have all the three angles equal to 60°.
(b) A triangle can have all the three angles greater than 60°.
(c) The sum of any two angles of a triangle is always greater than the third angle.
(d) The difference between the lengths of any two sides of a triangle is greater than the length of the third side.
17. Which of the following statement is false?
(a) The sum of the lengths of any two sides of a triangle is less than the third side.
(b) In a right-angled triangle, the square on the hypotenuse = sum of the squares on the legs.
(c) If the Pythagorean property holds, the triangle must be right-angled.
(d) The diagonal of a rectangle produce ‘by itself the same area as produced by its length and breadth.
18. Two angles of a triangle measure 90° and 30°. The measure of the third angle is
(a) 90°
(b) 30°
(c) 60°
(d) 120°.
19. The ratio of the measures of the three angles of a triangle is 2 : 3 : 4. The measure of the largest angle is
(a) 80°
(b) 60°
(c) 40°
(d) 180°.
20. In the following figure, the side BC of ∆ ABC is extended up to the point D. If ∠ A = 55° and ∠ B = 60°, then the measure of ∠ACD is
(a) 120°
(b) 110°
(c) 115°
(d) 125°.
21. In the following figure, the measure of ∠A is
(a) 30°
(b) 45°
(c) 90°
(d) 30°.
22. In the following figure, the measure of ∠A is
(a) 70°
(b) 90°
(c) 80°
(d) 100°.
23. In the following figure, m || QR. Then, the measure of ∠QPR is
(a) 80°
(b) 85°
(c) 75°
(d) 70°.
24. In the following figure, find ∠ x and ∠ y, if ∠x – ∠y – 10°
(a) 65°, 55°
(b) 55°, 45°
(c) 45°, 35°
(d) 60°, 60°.
25. In the following figure, find ∠ B.
(a) 30°
(b) 45°
(c) 40°
(d) 60°
26. In the following figure, ∆ ABC is an equilateral triangle. Find ∠x.
(a) 30°
(b) 45°
(c) 60°
(d) 90°
27. In the following figure, one angle of triangle ABC is 40°. If the difference of the other two angles is 30°, find the larger of the other two angles.
(a) 85°
(b) 80°
(c) 75°
(d) 70°.
28. In the following figure, find
(a) 60°
(b) 70°
(c) 80°
(d) 75°.
29. In the following figure, find x if BA || CE.
(a) 60°
(b) 40°
(c) 45°
(d) 65°
30. Find the value of the unknown interior angle x in the following figure:
(a) 30°
(b) 35°
(c) 40°
(d) 45°
31. Find the value of unknown x in the following figure:
(a) 40°
(b) 50°
(c) 45°
(d) 55°
32. Find the value of unknown x in the following figure:
(a) 10°
(b) 15°
(c) 20°
(d) 25°
33. Find angle x in the following figure:
(a) 90°
(b) 80°
(c) 95°
(d) 100°
34. Find angle x in the following figure:
(a) 40°
(b) 50°
(c) 45°
(d) 60°
35. Find angle x in the following figure:
(a) 40°
(b) 30°
(c) 25°
(d) 35°
36. Find angle x in the following figure:
(a) 40°
(b) 45°
(c) 35°
(d) 50°
37. Find angle x in the following figure:
(a) 58°
(b) 59°
(c) 57°
(d) 56°
38. Find angle x in the following figure:
(a) 45°
(b) 40°
(c) 35°
(d) 50°
39. In which case of the following lengths of sides of a triangle, is it possible to draw a triangle?
(а) 3 cm, 4 cm, 7 cm
(b) 2 cm, 3 cm, 7 cm
(c) 3 cm, 4 cm, 5 cm
(d) 3 cm, 3 cm, 7 cm.
40. Which of the following cannot be the sides of a right triangle?
(а) 2 cm, 2 cm, 4 cm
(b) 5 cm, 12 cm, 13 cm
(c) 6 cm, 8 cm, 10 cm
(d) 3 cm, 4 cm, 5 cm.
ANSWERS
HINTS/SOLUTIONS
1. See a triangle.
2. See a triangle.
3. See a triangle.
4. See a triangle.
5. Definition of a scalene triangle.
6. Definition of an isosceles triangle.
7. Definition of an equilateral triangle.
8. Definition of an acute-angled triangle.
9. Definition of a right triangle.
10. Definition of an obtuse angled triangle.
11. Draw medians and count.
12. Draw altitudes and count.
13. Angle Sum Property of a triangle.
14. x° + x° + x° = 180° ⇒ x° = 60°.
18. Third angle = 180° – (90° + 30°) = 60°.
19. Largest angle = 
20. ∠ ACD = 60° + 55° = 115°.
21. ∠ A – 180° – [(180° – 120°) + (180° – 120°)] = 60°.
22. ∠A – 180° – (60° + 40°) = 80°
23. ∠ PQR = 50°
∴ ∠ QPR – 180° – (50° + 45°) = 85°.
24. ∠x + ∠y = 120°; ∠x – ∠y = 10° Solve to get ∠x = 65°, ∠y = 55°.
25. ∠B = 180° – [(180° – 110°) + 50°] = 60°.
26. ∠ABC = 60°.
∴ ∠ABD = 180° – 60° = 120°
∴ x = 180° – (120° + 30°) = 30°.
27. x + y = 180° – 40° = 140° x – y = 30°. Solve to get x = 85°.
28. x + x = 140° ⇒ x = 70°.
29. ∠ECD = ∠ABC = 50°;
∴ x = 180° – (65° + 50°) = 65°.
30. x + 90° = 130° ⇒ x = 40°.
31. x + 40° + 90° = 180° ⇒ x = 50°.
32. x + 5x + 90° = 180° ⇒ x = 15°.
33. x + 45 + 45° = 180° ⇒ x = 90°.
34. x = 50°.
35. x + x + 120° = 180° ⇒ x = 30°.
36. x + 140° = 180° ⇒ x = 40°.
37. x + x = 116° ⇒ x = 58°.
38. x = 45°.
39. 3 + 4 > 5; 4 + 5 > 3; 5 + 3 > 4.
40. 22 + 22 = 8; 42 = 16
∴ 22 + 22 ≠ 42
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