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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-07-INE-01
Inequalities in a Triangle — Assignment
Chapter: Triangles
Topic: Inequalities in a Triangle
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.
The sum of any two sides is greater than the:
  • A.perimeter
  • B.third side
  • C.largest angle
  • D.area
2.
The difference of any two sides is less than the:
  • A.perimeter
  • B.third side
  • C.largest angle
  • D.area
3.
The greater angle is opposite the:
  • A.smaller side
  • B.greater side
  • C.base
  • D.median
4.
The greater side is opposite the:
  • A.smaller angle
  • B.greater angle
  • C.base
  • D.vertex
5.
Can sides $2,3,6$ form a triangle?
  • A.Yes
  • B.No
  • C.only if right
  • D.cannot tell
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Can sides $3,4,5$ form a triangle?
7.
Can sides $1,2,3$ form a triangle?
8.
In $\triangle ABC$, $\angle A>\angle B$. Which is longer, $BC$ or $AC$?
9.
The difference of two sides $10$ and $6$ is less than the:
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Two sides of a triangle are $8$ and $5$. The third side $x$ satisfies what inequality?
11.
In $\triangle ABC$, $AB=6,BC=8,CA=7$. Which is the largest angle?
12.
Can $4,6,11$ form a triangle?
13.
In $\triangle ABC$, $\angle A=80^\circ,\angle B=60^\circ$. Which side is longest?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The sides of a triangle are $7$ cm, $24$ cm and $x$ cm. Find the range of $x$.
15.
In $\triangle ABC$, $\angle A=70^\circ$ and $\angle B=60^\circ$. Arrange the sides in ascending order.

Answer Key

Section A — Multiple Choice Questions
  1. (B) third side
  2. (B) third side
  3. (B) greater side
  4. (B) greater angle
  5. (B) No
Section B — Short Answer (2 marks)
  1. Yes.
  2. No.
  3. $BC$ (opposite the greater angle).
  4. Third side.
Section C — Short Answer (3 marks)
  1. $3
  2. $\angle A$ (opposite $BC=8$).
  3. No ($4+6<11$).
  4. $BC$ (opposite $\angle A$).
Section D — Long Answer (5 marks)
  1. $17
  2. $AB
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