This set of Class 9 Maths Chapter 7 Multiple Choice Questions & Answers (MCQs) focuses on “Some More Criteria for Congruence of Triangles”.
1. From the following diagram, which of the following option is true?
a) ∠A = ∠Q, ∠B = R, ∠C = ∠P
b) ∠A = ∠P, ∠B = Q, ∠C = ∠R
c) ∠A = ∠R, ∠B = P, ∠C = ∠Q
d) ∠A = ∠R, ∠B = Q, ∠C = ∠P
View Answer
Explanation: As we can see that AB = PQ, BC = QR and CA = RP, according to SSS rule (Theorem 7.4), ΔABC and PQR are congruent and hence angles of ΔABC are equal to corresponding angles of ΔPQR.
Therefore, ∠A = ∠P, ∠B = Q, ∠C = ∠R.
2. From the diagram given below, we can say that ΔABC and ΔPQR are congruent.
a) True
b) False
View Answer
Explanation: We can see in the diagram that AB = PQ, ∠ABC = ∠PQR (Right angles) and BC = PR. Therefore, according to RHS rule (Theorem 7.5), ΔABC and ΔPQR are congruent.
3. From the diagram given below, what is the true relation between ∠ABC and ∠ABD?
a) ∠ABC = ∠ABD
b) ∠ABC > ∠ABD
c) ∠ABC < ∠ABD
d) Data is insufficient
View Answer
Explanation: We can see in the diagram that AD > AC and the angles opposite to sides AD and AC are ∠ABD and ∠ABC respectively.
Therefore, according to theorem 7.6, angle opposite to the longer side is larger.
Hence, ∠ABC < ∠ABD.
4. From the diagram given below, what is the true relation between three sides of the triangle?
a) AB + AC = BC
b) AB + BC = AC
c) AB + BC < AC
d) AB + BC > AC
View Answer
Explanation: According to theorem 7.8, sum of any two sides of a triangle is greater than third side.
Hence, AB + BC > AC is correct.
5. From the diagram given below, which of the following option is true?
a) ΔOBA and ΔOBC are congruent
b) ΔOBA and ΔOBC are not congruent
c) ∠ABO < ∠CBO
d) ∠ABO > ∠CBO
View Answer
Explanation: We can see in the diagram that AB = BC (given),
OB = OB (same side) and AO = OC (BO is bisector of the side AC).
Therefore, according to SSS rule, ΔOBA and ΔOBC are congruent.
Sanfoundry Global Education & Learning Series – Mathematics – Class 9.
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