Attempt the Class 7 Triangle and Its Properties question paper given above and then check the answers along with the step-by-step solutions of each question in the video provided below. Understanding the steps is very important in Mathematics, as proper stepwise solving helps in gaining step marking and improves overall problem-solving skills.
Section A: Multiple Choice Questions (1 × 10 = 10 marks)
- The sum of the interior angles of a triangle is:
(a) 90° (b) 120° (c) 180° (d) 360° - A triangle having all unequal sides is called:
(a) Isosceles (b) Equilateral (c) Scalene (d) Right - Which of the following sets of lengths can form a triangle?
(a) 2 cm, 3 cm, 6 cm
(b) 4 cm, 5 cm, 9 cm
(c) 5 cm, 7 cm, 10 cm
(d) 3 cm, 4 cm, 8 cm - The longest side of a right-angled triangle lies opposite the:
(a) Smallest angle
(b) Right angle
(c) Acute angle
(d) Obtuse angle - A triangle with angles 50°, 60°, and 70° is:
(a) Right-angled
(b) Obtuse-angled
(c) Acute-angled
(d) Isosceles - How many medians does a triangle have?
(a) 1 (b) 2 (c) 3 (d) 6 - In an equilateral triangle, the sides are:
(a) Unequal
(b) Pairwise equal
(c) All equal
(d) In ratio 1:2:3 - If one angle of a triangle is obtuse, the triangle is called:
(a) Acute-angled
(b) Right-angled
(c) Obtuse-angled
(d) Equilateral - Which property is used to check whether three lengths form a triangle?
(a) Pythagoras theorem
(b) Angle sum property
(c) Triangle inequality theorem
(d) SAS congruence - The sum of the lengths of any two sides of a triangle is always:
(a) Equal to the third side
(b) Less than the third side
(c) Greater than the third side
(d) Half of the third side
Note: Check the solutions to this question paper at the end of the paper.
Section B: Very Short Answer Questions (2 × 5 = 10 marks)
11. Find the third angle of a triangle if the other two angles are 48° and 62°.
12. State the angle sum property of a triangle.
13. How many altitudes does a triangle have? Write their names.
14. Can a triangle be formed with sides 6 cm, 9 cm, and 15 cm? Give reason.
15. Define an obtuse-angled triangle with an example.
16. In the given figure, if ∠b = 60° and ∠c = 65°, find the measures of ∠d and ∠a.
17. Find the value of angle x in the given figure.
18. If E is the midpoint of BC, name the median and the altitude of triangle ABC.
Section C: Short Answer Questions (3 × 6 = 18 marks)
19. The angles of a triangle are in the ratio 1 : 2 : 3. Find the angles.
20. Find the perimeter of an isosceles triangle whose equal sides are 10 cm each and base is 12 cm.
21. The sides of a triangle are 7 cm, 24 cm, and 25 cm. Check whether the triangle is right-angled.
22. If one angle of an equilateral triangle is 60°, find the remaining angles and justify your answer.
23. The perimeter of a triangle is 30 cm. Two sides measure 9 cm and 11 cm.
Find the third side and check whether the triangle is possible.
24. In a triangle, one angle is twice the second angle and the third angle is 30°. Find all the angles of the triangle.
25. In the given figure, find the value of a, b, and c.
Section D: Long Answer Questions (5 × 2 = 10 marks)
26. The sides of a triangle are 8 cm, 15 cm, and 17 cm.
(a) Name the type of triangle
(b) Verify whether it satisfies Pythagoras theorem
27. The angles of a triangle are in arithmetic progression. If the middle angle is 60°, find all the angles of the triangle.
