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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-07-CON-01
Congruence of Triangles — Assignment
Chapter: Triangles
Topic: Congruence of Triangles and Criteria for Congruence
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Congruent triangles have equal corresponding sides and:
  • A.areas only
  • B.angles
  • C.perimeters
  • D.medians
2.
SAS stands for:
  • A.Side-Angle-Side
  • B.Side-Area-Side
  • C.Sum-Angle-Sum
  • D.Side-Altitude-Side
3.
The symbol for congruence is:
  • A.$\sim$
  • B.$\cong$
  • C.$=$
  • D.$\parallel$
4.
ASA uses two angles and the:
  • A.opposite side
  • B.included side
  • C.hypotenuse
  • D.largest side
5.
RHS applies to:
  • A.all triangles
  • B.right triangles
  • C.equilateral
  • D.obtuse
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Name the congruence criterion that uses all three sides.
7.
If $\triangle ABC\cong\triangle DEF$ and $AB=5$, find $DE$.
8.
State the criterion using two angles and the included side.
9.
Are all congruent triangles also similar?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
State the SAS congruence rule.
11.
In $\triangle ABC\cong\triangle PQR$, if $\angle A=50^\circ$, find $\angle P$.
12.
State the RHS congruence rule.
13.
Why is AAA not a congruence criterion?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
In $\triangle ABC$ and $\triangle DEF$, $AB=DE$, $\angle B=\angle E$ and $BC=EF$. State the congruence rule and one conclusion.
15.
State the result: the angles opposite equal sides of an isosceles triangle.

Answer Key

Section A — Multiple Choice Questions
  1. (B) angles
  2. (A) Side-Angle-Side
  3. (B) $\cong$
  4. (B) included side
  5. (B) right triangles
Section B — Short Answer (2 marks)
  1. SSS.
  2. $5$.
  3. ASA.
  4. Yes.
Section C — Short Answer (3 marks)
  1. Two sides and the included angle of one equal the corresponding parts of the other.
  2. $50^\circ$.
  3. In right triangles, the hypotenuse and one side equal the corresponding parts.
  4. It guarantees only similarity, not equal size.
Section D — Long Answer (5 marks)
  1. SAS; $\triangle ABC\cong\triangle DEF$, so $AC=DF$.
  2. They are equal (base angles equal).
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