Class 9 Inequalities Mock Test (ICSE)

Topics in Inequalities

• Greater side opposite greater angle
• Greater angle opposite greater side
• Sum of two sides greater than the third
• Perpendicular is the shortest line segment

Inequalities practice questions with answers

1. Q1Multiple choice·1 mark
   Which of the following sets of side lengths can form a valid triangle?

   1. (a)$5\text{ cm}, 8\text{ cm}, 12\text{ cm}$
   2. (b)$2\text{ cm}, 4\text{ cm}, 7\text{ cm}$
   3. (c)$2\text{ cm}, 3\text{ cm}, 6\text{ cm}$
   4. (d)$3\text{ cm}, 4\text{ cm}, 7\text{ cm}$
   Show answer and step marks

   1. Correct option: (a) $5\text{ cm}, 8\text{ cm}, 12\text{ cm}$+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   In $\triangle PQR$, if $PQ = 6\text{ cm}$, $QR = 7\text{ cm}$, and $PR = 5\text{ cm}$, which of the following gives the correct order of its interior angles?

   1. (a)$\angle P < \angle R < \angle Q$
   2. (b)$\angle Q < \angle R < \angle P$
   3. (c)$\angle P < \angle Q < \angle R$
   4. (d)$\angle Q < \angle P < \angle R$
   Show answer and step marks

   1. Correct option: (b) $\angle Q < \angle R < \angle P$+1

   Answer: (b)
3. Q3Multiple choice·1 mark
   From a point $P$ outside a line $l$, a perpendicular $PQ$ and several oblique line segments $PR$, $PS$, and $PT$ are drawn to line $l$. Which of the following relations is always true?

   1. (a)$PQ = PR$
   2. (b)$PS < PQ$
   3. (c)$PR < PQ$
   4. (d)$PQ < PR$
   Show answer and step marks

   1. Correct option: (d) $PQ < PR$+1

   Answer: (d)
4. Q4Multiple choice·1 mark
   In $\triangle ABC$, if $\angle A = 50^\circ$ and $\angle B = 70^\circ$, which of the following is the correct relation between the sides of the triangle?

   1. (a)$AC < BC < AB$
   2. (b)$BC < AC < AB$
   3. (c)$AB < BC < AC$
   4. (d)$BC < AB < AC$
   Show answer and step marks

   1. Correct option: (d) $BC < AB < AC$+1

   Answer: (d)

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