This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Congruence of Triangle – 1”.
1. Given that ∠A = ∠P and AC = PR. Then, which of the following conditions are true for Δ PQR and Δ ABC to be congruent.
a) BC = QR by ASS criteria
b) BC = QR by SSA criteria
c) AB = PQ by SAS criteria
d) AB = PQ by SSA criteria
Explanation: If two sides and the included angle of a triangle is equal to the two sides and the included angle of another triangle, then the two triangles are said to be congruent by SAS congruence criteria. Only SAS congruence criteria holds true not ASS or SSA rule.
In Δ PQR and Δ ABC,
∠P = ∠A (given),
AC = PR (given),
Δ PQR and Δ ABC will be congruent by SAS rule only when AB = PQ.
2. Find the angle ∠Q and ∠R if ∠P = 80° and PQ = PR.
Explanation: In Δ PQR, ∠P = 80° (Given)
And PQ = PR (Given)
⇒ ∠Q = ∠R (Angles opposite to two equal sides of triangle are equal)
Now, ∠P + ∠Q + ∠R = 180° (Angle Sum property of triangle)
⇒ 80° + 2∠Q = 180° (∠Q = ∠R)
⇒ 2∠Q = 100°
⇒ ∠Q = 50°
Hence, ∠Q = ∠R = 50°.
3. Find the value of angle ABC if AB = BC.
Explanation: From Figure, ∠BAC + ∠CAD = 180° (Linear Pair)
⇒ ∠BAC + 100° = 180°
⇒ ∠BAC = 80°
In Δ ABC, ∠BAC = 80° (from above equation)
And AB = BC (Given)
⇒ ∠A = ∠C (Angles opposite to two equal sides of triangle are equal)
∠BAC + ∠ABC + ∠ACB = 180° (Angle Sum property of triangle)
⇒ 80° + ∠B + 80° = 180°
⇒ ∠B = 180° – 160°
⇒ ∠B = 20°.
4. Identify the rule by which the following triangles are congruent.
Explanation: From Figure, In Δ PQR and Δ PSR,
∠Q = ∠S = 90° (given),
PQ = PS = 4cm (given), and
PR = PR (Common side)
Hence, Δ PQR is congruent to Δ PSR by RHS Congruence rule.
5. The following triangles are congruent under PRQ ↔ XYZ. Which part of Δ XYZ correspond to PQ?
Explanation: As triangle PRQ is congruent to triangle XYZ,
PR ↔ XY, PQ ↔ XZ, RQ ↔ YZ, and
∠P ↔ ∠X, ∠R ↔ ∠Y, ∠Q ↔ ∠Z (Corresponding parts of congruent triangles)
Hence, Side XZ corresponds to side PQ.
6. Which of the following relation is correct if PQ = PS, PR = PT and ∠QPS = ∠TPR?
a) QR = ST
b) QR > ST
c) QR < ST
d) QR = QP
Explanation: As it is given that, PQ = PS, PR = PT and ∠QPS = ∠TPR,
∆ PQR is congruent to Δ PST by SAS congruence rule.
Hence, QR = ST (Corresponding parts of congruent triangles).
7. Which among the following relation is correct?
a) Δ ABC ≅ Δ DEF
b) Δ ACB ≅ Δ EFD
c) Δ ABC ≅ Δ FED
d) Δ ACB ≅ Δ FED
Explanation: From Figure, In Δ ABC and Δ DEF,
∠BAC = ∠DFE = 40°,
∠ACB = ∠DEF = 60° and
AC = EF
Hence, Δ ACB ≅ Δ FED by ASA congruence criteria.
Sanfoundry Global Education & Learning Series – Mathematics – Class 9.
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