Properties of triangles and Pythagoras Quiz - ICSE Class 7 Mathematics

Free practice quiz: Properties of triangles and Pythagoras (ICSE Class 7 Mathematics). 56 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 7 Mathematics practice quiz has 56 multiple-choice questions on Properties of triangles and Pythagoras, and 55 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. In triangle ABC, if angle A = 70 degrees and angle B = 50 degrees, what is the measure of angle C?

   1. 40 degrees
   2. 50 degrees
   3. 60 degrees
   4. 70 degrees
   Show answer

   Answer: C. 60 degrees

   The sum of angles in a triangle is always 180 degrees. Therefore, angle C = 180 - (angle A + angle B) = 180 - (70 + 50) = 180 - 120 = 60 degrees.

2. If the sides of a triangle are 9 cm, 12 cm, and 15 cm, what is the nature of the triangle?

   1. Acute-angled
   2. Obtuse-angled
   3. Right-angled
   4. Cannot form a triangle
   Show answer

   Answer: C. Right-angled

   We check if the Pythagorean theorem holds: 9² + 12² = 81 + 144 = 225. And 15² = 225. Since 9² + 12² = 15², it is a right-angled triangle.

3. What is the perimeter of a triangle with sides 6 cm, 8 cm, and 10 cm?

   1. 20 cm
   2. 24 cm
   3. 30 cm
   4. 36 cm
   Show answer

   Answer: B. 24 cm

   The perimeter of a triangle is the sum of the lengths of its three sides. Perimeter = 6 cm + 8 cm + 10 cm = 24 cm.

4. If a triangle has sides 5 cm, 8 cm, and 11 cm, which statement is true?

   1. It is an equilateral triangle.
   2. It is an isosceles triangle.
   3. It is a scalene triangle.
   4. It cannot form a triangle.
   Show answer

   Answer: C. It is a scalene triangle.

   A scalene triangle has all sides of different lengths. Since 5 cm, 8 cm, and 11 cm are all different, the triangle is scalene. Also, 5+8 > 11 (13>11), satisfying the triangle inequality.

5. In triangle ABC, if angle A = 50 degrees and angle C = 80 degrees, what is the measure of angle B?

   1. 40 degrees
   2. 50 degrees
   3. 60 degrees
   4. 70 degrees
   Show answer

   Answer: B. 50 degrees

   The sum of angles in a triangle is 180 degrees. Angle B = 180 - (angle A + angle C) = 180 - (50 + 80) = 180 - 130 = 50 degrees. This makes the triangle isosceles.

More questions in this quiz

Answers and explanations are in the full quiz.

1. Which of the following sets of side lengths can form a triangle?
2. If a right-angled triangle has legs of length 6 units and 8 units, what is the length of the hypotenuse?
3. An isosceles triangle has two equal angles measuring 55 degrees each. What is the measure of the third angle?
4. In triangle PQR, PQ = 10 cm, QR = 12 cm, and PR = 14 cm. Which type of triangle is this based on its sides?
5. If the hypotenuse of a right-angled triangle is 25 cm and one leg is 7 cm, what is the length of the other leg?
6. What is the sum of the angles in any triangle?
7. A triangle has angles measuring 30 degrees, 60 degrees, and 90 degrees. What type of triangle is it?
8. If one side of an equilateral triangle is 5 cm, what are the lengths of the other two sides?
9. Which of the following is NOT a property of an isosceles triangle?
10. In a triangle ABC, if angle A = angle B = angle C, what is the measure of each angle?
11. Which of the following is a property of a scalene triangle?
12. In triangle XYZ, if angle X = 45 degrees and angle Y = 75 degrees, what is the measure of angle Z?
13. If a right-angled triangle has a hypotenuse of length 13 units and one leg of length 5 units, what is the length of the other leg?
14. Which of the following is NOT a valid set of angles for a triangle?
15. If one leg of a right-angled triangle is 3 units and the hypotenuse is 5 units, what is the length of the other leg?
16. In triangle PQR, angle P = 90 degrees, PQ = 5 cm, and PR = 12 cm. What is the length of QR?
17. An isosceles triangle has angles measuring x, x, and 2x degrees. What is the value of x?
18. Which statement is true about the angles of an acute-angled triangle?
19. If a triangle has sides of length 7 cm, 7 cm, and 10 cm, what type of triangle is it?
20. In a triangle ABC, angle A = 80 degrees and angle B = 80 degrees. What is the measure of angle C?
21. If a triangle has sides 5, 5, and 5, what is it called?
22. In a right-angled triangle, the square of the hypotenuse is equal to:
23. If one angle of an isosceles triangle is 100 degrees, what are the other two angles?
24. Which of these combinations of side lengths can form a triangle?
25. If a right-angled triangle has legs of length 7 cm and 24 cm, what is the length of the hypotenuse?
26. An obtuse-angled triangle has:
27. In triangle ABC, angle A = 55 degrees and angle B = 65 degrees. What is the measure of angle C?
28. If the hypotenuse of a right-angled triangle is 17 cm and one leg is 15 cm, what is the length of the other leg?
29. Which of the following describes an isosceles triangle?
30. In triangle XYZ, angle X = 30 degrees and angle Y = 90 degrees. What is the measure of angle Z?
31. In a right-angled triangle, if the hypotenuse is 26 cm and one leg is 10 cm, what is the length of the other leg?
32. Which of the following is a characteristic of an equilateral triangle?
33. If a triangle has angles 30 degrees, 30 degrees, and 120 degrees, what type of triangle is it?
34. In triangle ABC, angle A = 40 degrees and angle B = 70 degrees. What is the measure of angle C?
35. Which of the following side lengths can form a triangle?
36. If a right-angled triangle has legs of length 9 cm and 40 cm, what is the length of the hypotenuse?
37. In triangle ABC, angle A = 30 degrees and angle B = 60 degrees. What is the measure of angle C?
38. Which statement is always true for any triangle?
39. If a triangle has angles 110 degrees, 35 degrees, and 35 degrees, what type of triangle is it?
40. What is the length of the hypotenuse of a right-angled triangle with legs of length 8 cm and 15 cm?
41. Which of these side lengths CANNOT form a triangle?
42. In a triangle PQR, angle P = 45 degrees and angle Q = 45 degrees. What type of triangle is it?
43. If a right-angled triangle has legs of length 11 cm and 60 cm, what is the length of the hypotenuse?
44. What is the property of a triangle with angles 90, 45, 45 degrees?
45. If a triangle has sides 13 cm, 14 cm, and 15 cm, what type of triangle is it based on its angles?
46. In triangle ABC, angle A = 120 degrees. What can be said about angles B and C?
47. If one leg of a right-angled triangle is equal to the hypotenuse, what can you say about the other leg?
48. What is the sum of the exterior angles of any triangle, taking one at each vertex?
49. If a triangle has sides of length 4 cm, 4 cm, and 4 cm, what is its perimeter?
50. Which of the following sets of side lengths CANNOT form a triangle?
51. In a triangle, if one angle is 90 degrees and another is 30 degrees, what is the third angle?

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