Mathematics Questions and Answers – Some More Criteria for Congruence of Triangles

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This set of Mathematics Problems for Class 9 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

Answer: b
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.
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2. From the diagram given below, we can say that ΔABC and ΔPQR are congruent.

a) True
b) False
View Answer

Answer: a
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

Answer: c
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.
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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

Answer: d
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

Answer: a
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.
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Sanfoundry Global Education & Learning Series – Mathematics – Class 9.

To practice Mathematics Problems for Class 9, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter