Congruency of Triangles Quiz - ICSE Class 9 Mathematics

Free practice quiz: Congruency of Triangles (ICSE Class 9 Mathematics). 34 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This ICSE Class 9 Mathematics practice quiz has 34 multiple-choice questions on Congruency of Triangles, and 34 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 AB = AC and angle BAC = 80 degrees, find the measure of angle ABC.

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

   Answer: B. 50 degrees

   Since AB = AC, triangle ABC is an isosceles triangle. Therefore, angle ABC = angle ACB. The sum of angles in a triangle is 180 degrees. So, angle ABC + angle ACB + angle BAC = 180 degrees. 2 * angle ABC + 80 degrees = 180 degrees. 2 * angle ABC = 100 degrees. angle ABC = 50 degrees.

2. Which of the following is NOT a criterion for congruence of triangles?

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

   Answer: C. AAA

   The standard congruence criteria for triangles are SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side). AAA (Angle-Angle-Angle) only proves similarity, not congruence, because triangles with the same angles can have different sizes.

3. If triangle MNO is congruent to triangle PQR, which of the following statements is necessarily true?

   1. MN = PR
   2. NO = PQ
   3. MO = QR
   4. MN = PQ
   Show answer

   Answer: D. MN = PQ

   For congruent triangles, corresponding sides are equal. If triangle MNO is congruent to triangle PQR, then M corresponds to P, N to Q, and O to R. Therefore, MN = PQ, NO = QR, and MO = PR.

4. If triangle ABC is congruent to triangle XYZ by SSS criterion, and AB = 8 cm, BC = 9 cm, AC = 10 cm, then what is XY + YZ + XZ?

   1. 18 cm
   2. 27 cm
   3. 30 cm
   4. 29 cm
   Show answer

   Answer: B. 27 cm

   By SSS congruence, AB = XY, BC = YZ, and AC = XZ. Therefore, XY = 8 cm, YZ = 9 cm, and XZ = 10 cm. The sum XY + YZ + XZ = 8 + 9 + 10 = 27 cm.

5. In triangles ABC and XYZ, AB = XY, BC = YZ, and angle B = angle Y. This implies congruence by which criterion?

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

   Answer: A. SAS

   The given information is Side (AB=XY), Angle (angle B = angle Y), and Side (BC=YZ). Since the angle is included between the two sides, this satisfies the Side-Angle-Side (SAS) congruence criterion.

More questions in this quiz

Answers and explanations are in the full quiz.

1. If triangle PQR is congruent to triangle XYZ by SSS criterion, then which of the following is true?
2. Two triangles ABC and PQR are such that AB = PQ, BC = QR, and AC = PR. Which congruence criterion applies?
3. In triangles ABC and XYZ, if angle A = angle X, AC = XZ, and BC = YZ, which congruence criterion can be used to prove the triangles are congruent?
4. If two angles and the included side of one triangle are equal to the corresponding two angles and the included side of another triangle, the triangles are congruent by which criterion?
5. In triangle PQR, PQ = PR and angle Q = 50 degrees. Find angle P.
6. If triangle ABC is congruent to triangle XYZ by SAS criterion, and AB = 5 cm, angle B = 60 degrees, BC = 7 cm, then which of the following is true?
7. In triangle ABC, AD is the angle bisector of angle A. If AB = 6 cm and AC = 8 cm, what is the ratio BD:DC?
8. Two triangles ABC and DEF are congruent. If angle A = 45 degrees and angle B = 55 degrees, what is the measure of angle F?
9. In triangle XYZ, if XY = XZ and angle Y = 70 degrees, then angle YXZ is:
10. If triangle ABC is congruent to triangle PQR by ASA criterion, and angle A = 70 degrees, AC = 10 cm, angle C = 60 degrees, then which of the following is true?
11. In triangle ABC, if AB = AC and angle BAC = 40 degrees, find the measure of angle ABC.
12. In triangle ABC, AD is the altitude to BC. If AB = 13 cm, AC = 15 cm, and BC = 14 cm, find the length of AD.
13. If two angles of a triangle are 30 degrees and 70 degrees, what is the third angle?
14. In isosceles triangle ABC, AB = AC. If angle ABC = angle ACB = 50 degrees, what is angle BAC?
15. If triangle ABC is congruent to triangle DEF by AAS criterion, and angle A = 65 degrees, angle B = 45 degrees, then which of the following is true about triangle DEF?
16. Which of the following conditions guarantees that two triangles are congruent?
17. In triangles PQR and XYZ, if PQ = XY, angle P = angle X, and PR = XZ, which congruence criterion applies?
18. In triangle ABC, AB || DE and AC || FG. If triangle ABC is congruent to triangle DEF, which of the following must be true?
19. Two triangles have equal corresponding angles. Are they necessarily congruent?
20. In triangle ABC, angle A = 90 degrees, AB = 5 cm, AC = 12 cm. If triangle ABC is congruent to triangle PQR by RHS criterion, what is the length of the hypotenuse of triangle PQR?
21. If triangle ABC is congruent to triangle XYZ by AAS criterion, and angle A = 50 degrees, angle C = 70 degrees, then which of the following is true?
22. In triangle ABC, D is a point on BC such that AD bisects angle BAC. If AB=10, AC=15, BD=4, then DC is:
23. If triangle PQR is congruent to triangle STU, and PQ = 7, QR = 8, PR = 9. What is the perimeter of triangle STU?
24. If triangle ABC is congruent to triangle XYZ by ASA criterion, and angle A = 40 degrees, AB = 6 cm, angle B = 70 degrees, then what is angle Y and side YZ?
25. In triangle ABC, AB = AC and angle ABC = 50 degrees. What is the measure of angle BAC?
26. If triangle ABC is congruent to triangle PQR by SAS criterion, and AB = 8 cm, angle B = 60 degrees, BC = 7 cm, what is the value of angle R?
27. In triangles ABC and XYZ, AC = XZ, BC = YZ, and angle C = angle Z. This implies congruence by which criterion?
28. If triangle ABC is congruent to triangle XYZ by SSS criterion, and AB=10, BC=12, AC=14. What is XY + YZ + XZ?
29. Which of the following implies that triangle ABC is congruent to triangle XYZ?

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