Triangles Quiz - ICSE Class 8 Mathematics

Free practice quiz: Triangles (ICSE Class 8 Mathematics). 58 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 8 Mathematics practice quiz has 58 multiple-choice questions on Triangles, and 58 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 = 55°, angle B = 65°, then what is the measure of angle C?

   1. 60°
   2. 70°
   3. 50°
   4. 80°
   Show answer

   Answer: A. 60°

   The sum of angles in a triangle is always 180°. Therefore, angle C = 180° - (angle A + angle B) = 180° - (55° + 65°) = 180° - 120° = 60°.

2. Which congruence criterion is satisfied by two triangles if their three sides are respectively equal?

   1. ASA
   2. AAS
   3. SSS
   4. RHS
   Show answer

   Answer: C. SSS

   SSS stands for Side-Side-Side. This congruence criterion states that if the three sides of one triangle are equal to the corresponding three sides of another triangle, then the two triangles are congruent.

3. Which of the following congruence criteria involves two angles and a non-included side?

   1. SAS
   2. ASA
   3. AAS
   4. SSS
   Show answer

   Answer: C. AAS

   AAS stands for Angle-Angle-Side. This congruence criterion states that if two angles and a non-included side of one triangle are equal to the corresponding two angles and non-included side of another triangle, then the triangles are congruent.

4. In triangle ABC, angle B = 90°. If AB = 3 cm and BC = 4 cm, what is the length of AC?

   1. 5 cm
   2. 6 cm
   3. 7 cm
   4. 8 cm
   Show answer

   Answer: A. 5 cm

   Using the Pythagorean theorem, $AC^2 = AB^2 + BC^2 = 3^2 + 4^2 = 9 + 16 = 25$. Therefore, AC = $\sqrt{25} = 5$ cm.

5. If triangle ABC is congruent to triangle XYZ, and BC = 9 cm, AC = 11 cm, AB = 13 cm, then what is the length of XZ?

   1. 9 cm
   2. 11 cm
   3. 13 cm
   4. Cannot be determined
   Show answer

   Answer: B. 11 cm

   The congruence statement triangle ABC is congruent to triangle XYZ implies that AC corresponds to XZ. Therefore, XZ = AC = 11 cm.

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. An isosceles triangle has one angle measuring 100°. What are the measures of the other two angles?
3. If triangle PQR is congruent to triangle XYZ, which of the following is true?
4. In a right-angled triangle, if one acute angle is 30°, what is the measure of the other acute angle?
5. What is the property that states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent?
6. An equilateral triangle has all sides equal to 9 cm. What is the measure of each angle?
7. In triangle ABC, AB = AC and angle B = 50°. What is the measure of angle A?
8. If triangle ABC is congruent to triangle DEF, then which angle corresponds to angle B?
9. The exterior angle of a triangle is equal to the sum of:
10. In triangle MNO, angle M = 75° and angle N = 45°. What is the measure of the exterior angle at vertex O?
11. If triangle ABC is congruent to triangle PQR, and AB = 5 cm, BC = 7 cm, AC = 9 cm, then what is the length of PQ?
12. In triangle XYZ, angle X = 90° and angle Y = 45°. What is the measure of angle Z?
13. Which property states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent?
14. An isosceles triangle has two equal angles of 55° each. What is the measure of the third angle?
15. If triangle ABC is congruent to triangle BCA, which of the following is necessarily true?
16. In triangle ABC, angle A = 60°, angle B = 70°. If we draw a line segment AD such that D is on BC and angle CAD = 20°, what is the measure of angle BAD?
17. Two triangles are congruent if one angle and the two sides including it are equal to the corresponding angles and sides. This is known as:
18. In triangle ABC, angle A = 90°. If AB = 6 cm and AC = 8 cm, what is the length of BC (hypotenuse)?
19. If triangle PQR is congruent to triangle STU, which side corresponds to QR?
20. What is the sum of the interior angles of a triangle?
21. In triangle ABC, if angle A = 40° and angle B = 60°, what is the measure of the exterior angle at vertex C?
22. In an isosceles triangle, the vertex angle is 30°. What are the measures of the base angles?
23. If triangle ABC is congruent to triangle XYZ by SSS, and AB = 7 cm, BC = 8 cm, AC = 9 cm, then what is the length of YZ?
24. In a right-angled triangle, the angles are in the ratio 1:2:3. What are the angles?
25. Which congruence criterion states that if two angles and a side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent?
26. In triangle ABC, AB = BC = AC. What type of triangle is it?
27. If triangle ABC is congruent to triangle DEF, then which angle corresponds to angle C?
28. The sum of any two sides of a triangle is always ______ the third side.
29. In triangle PQR, PQ = PR and angle Q = 70°. What is the measure of angle P?
30. If triangle XYZ is congruent to triangle ABC by AAS, and angle X = 50°, angle Y = 60°, XY = 8 cm, then which side corresponds to XY?
31. What is the length of the hypotenuse of a right-angled triangle with legs of length 5 cm and 12 cm?
32. Two triangles are congruent if their corresponding sides are equal. This is known as:
33. In triangle PQR, angle P = 50°, angle Q = 50°. What type of triangle is it?
34. If triangle ABC is congruent to triangle XYZ, which angle corresponds to angle A?
35. In triangle ABC, angle A = 50°, angle B = 80°. What is the measure of angle C?
36. Which of the following is NOT a criterion for the congruence of triangles?
37. In triangle ABC, angle A = 70° and angle B = 60°. If CD is the altitude from C to AB, what is the measure of angle ACD?
38. In triangle ABC, angle A = 50°, angle B = 60°. CD is the altitude from C to AB. What is angle ACD?
39. If triangle ABC is congruent to triangle PQR by ASA, and angle A = 70°, angle B = 50°, AB = 10 cm, what is the measure of angle P?
40. In triangle XYZ, XY = YZ. If angle Z = 65°, what is the measure of angle Y?
41. Which of the following sets of side lengths can NOT form a triangle?
42. In a right-angled triangle, if one acute angle is 45°, what is the measure of the other acute angle?
43. In triangle ABC, angle A = 90°. If AB = 5 cm and BC = 13 cm, what is the length of AC?
44. What is the congruence criterion that uses two sides and a non-included angle?
45. In triangle ABC, AB = AC and angle A = 80°. What are the measures of angle B and angle C?
46. If triangle PQR is congruent to triangle STU, and angle P = 70°, angle Q = 50°, then what is the measure of angle T?
47. In a triangle, if one side is extended, the exterior angle formed is equal to the sum of the two interior opposite angles. This is known as:
48. Which congruence criterion requires that the hypotenuse and one side of a right-angled triangle are equal to the hypotenuse and corresponding side of another right-angled triangle?
49. In triangle ABC, AB = 10 cm, BC = 12 cm, AC = 14 cm. If triangle ABC is congruent to triangle XYZ by SSS, what is the perimeter of triangle XYZ?
50. In triangle ABC, angle A = 70°, angle B = 50°. If AD is the altitude from A to BC, what is angle ADB?
51. If triangle ABC is congruent to triangle PQR, and angle A = 70°, angle B = 50°, then what is the measure of angle R?
52. In triangle ABC, AB = BC. If angle ACB = 45°, what is the measure of angle ABC?
53. Which property is used to show that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar?

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