Class 9 Pythagoras Theorem Mock Test (ICSE)

Topics in Pythagoras Theorem

• Proof of Pythagoras theorem
• Converse of Pythagoras theorem
• Applications to right triangles

Pythagoras Theorem practice questions with answers

1. Q1Multiple choice·1 mark
   Which of the following sets of side lengths forms a right-angled triangle?

   1. (a)$5\text{ cm}, 12\text{ cm}, 13\text{ cm}$
   2. (b)$3\text{ cm}, 4\text{ cm}, 6\text{ cm}$
   3. (c)$2\text{ cm}, 3\text{ cm}, 4\text{ cm}$
   4. (d)$6\text{ cm}, 8\text{ cm}, 11\text{ cm}$
   Show answer and step marks

   1. Correct option: (a) $5\text{ cm}, 12\text{ cm}, 13\text{ cm}$ as $5^2 + 12^2 = 25 + 144 = 169 = 13^2$.+1

   Answer: (a)
2. Q2Multiple choice·1 mark
   In $\triangle PQR$, if $PQ^2 + QR^2 = PR^2$, then which of the following angles is $90^\circ$?

   1. (a)$\angle P$
   2. (b)$\angle Q$
   3. (c)$\angle R$
   4. (d)None of these
   Show answer and step marks

   1. Correct option: (b) $\angle Q$, because by the converse of Pythagoras theorem, if the sum of the squares of two sides equals the square of the third side, the angle opposite to the longest side $PR$ is a right angle, which is $\angle Q$.+1

   Answer: (b)
3. Q3Multiple choice·1 mark
   The length of a rectangle is $24\text{ cm}$ and its diagonal is $26\text{ cm}$. Find its breadth.

   1. (a)$10\text{ cm}$
   2. (b)$12\text{ cm}$
   3. (c)$5\text{ cm}$
   4. (d)$13\text{ cm}$
   Show answer and step marks

   1. Correct option: (a) $10\text{ cm}$ since breadth = $\sqrt{26^2 - 24^2} = \sqrt{676 - 576} = \sqrt{100} = 10\text{ cm}$.+1

   Answer: (a)
4. Q4Multiple choice·1 mark
   In a right-angled triangle $\triangle ABC$, right-angled at $B$, $BD \perp AC$ is drawn. Which of the following relations is correct?

   1. (a)$BC^2 = AD \cdot DC$
   2. (b)$BD^2 = AD \cdot AB$
   3. (c)$AB^2 = AD \cdot AC$
   4. (d)$AC^2 = AB \cdot BC$
   Show answer and step marks

   1. Correct option: (c) $AB^2 = AD \cdot AC$ derived from $\triangle ADB \sim \triangle ABC$.+1

   Answer: (c)

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