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.

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
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   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
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   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
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   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
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   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
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   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.

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