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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-07-PRP-01
Properties of a Triangle — Assignment
Chapter: Triangles
Topic: Properties of a Triangle: Angles and Sides
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.
In an isosceles triangle, the base angles are:
  • A.unequal
  • B.equal
  • C.right
  • D.supplementary
2.
The angle opposite the longest side is the:
  • A.smallest
  • B.largest
  • C.right
  • D.base
3.
The sum of two sides is ___ the third side.
  • A.less than
  • B.greater than
  • C.equal to
  • D.half
4.
In an equilateral triangle, each angle is:
  • A.$45^\circ$
  • B.$60^\circ$
  • C.$90^\circ$
  • D.$30^\circ$
5.
The side opposite the largest angle is the:
  • A.shortest
  • B.longest
  • C.base
  • D.median
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
An isosceles triangle has vertex angle $40^\circ$. Find each base angle.
7.
The angles are $50^\circ,60^\circ,70^\circ$. Which side is longest?
8.
Two sides are $5$ and $8$. The third side is less than:
9.
Each angle of an equilateral triangle is:
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
In $\triangle ABC$, $AB=AC$ and $\angle B=50^\circ$. Find $\angle A$.
11.
The angles are $30^\circ,60^\circ,90^\circ$. Order the sides from shortest to longest.
12.
Two sides are $7$ cm and $10$ cm. Between what values does the third side lie?
13.
The vertex angle of an isosceles triangle is $100^\circ$. Find the base angles.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
In $\triangle ABC$, $AB=AC$ and the bisector of $\angle A$ meets $BC$ at $D$. State what can be concluded about $BD$ and $DC$.
15.
Two sides of a triangle are $12$ cm and $15$ cm. Between what two values must the third side lie?

Answer Key

Section A — Multiple Choice Questions
  1. (B) equal
  2. (B) largest
  3. (B) greater than
  4. (B) $60^\circ$
  5. (B) longest
Section B — Short Answer (2 marks)
  1. $70^\circ$.
  2. The side opposite $70^\circ$.
  3. $13$.
  4. $60^\circ$.
Section C — Short Answer (3 marks)
  1. $80^\circ$.
  2. Opposite $30^\circ$, then $60^\circ$, then $90^\circ$.
  3. Between $3$ cm and $17$ cm.
  4. $40^\circ$ each.
Section D — Long Answer (5 marks)
  1. $BD=DC$ (D is the midpoint).
  2. Greater than $3$ cm and less than $27$ cm.
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