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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-23-STP-01
Pythagoras Theorem - Statement & Proof - Assignment
Chapter: Pythagoras Theorem
Topic: Statement and Proof of Pythagoras Theorem
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.
$(\text{hypotenuse})^2=$
  • A.$(\text{base})^2-(\text{height})^2$
  • B.$(\text{base})^2+(\text{height})^2$
  • C.$\text{base}+\text{height}$
  • D.$2bh$
2.
The side opposite the right angle is the:
  • A.base
  • B.height
  • C.hypotenuse
  • D.median
3.
For legs $3,4$, the hypotenuse is:
  • A.$5$
  • B.$6$
  • C.$7$
  • D.$12$
4.
The hypotenuse is the ___ side.
  • A.shortest
  • B.middle
  • C.longest
  • D.equal
5.
Is $5,12,13$ a right triangle?
  • A.Yes
  • B.No
  • C.Only if equilateral
  • D.Cannot say
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the hypotenuse of a right triangle with legs $6$ and $8$.
7.
Find the hypotenuse with legs $5$ and $12$.
8.
State Pythagoras' theorem.
9.
Name the longest side of a right triangle.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the hypotenuse with legs $9$ and $12$.
11.
One leg is $8$, hypotenuse $17$; find the other leg.
12.
Find the hypotenuse with legs $7$ and $24$.
13.
Is $8,15,17$ a right triangle?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A right triangle has legs $20$ cm and $21$ cm. Find the hypotenuse.
15.
The hypotenuse of a right triangle is $25$ cm and one leg is $7$ cm. Find the other leg and the area.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $(\text{base})^2+(\text{height})^2$
  2. (C) hypotenuse
  3. (A) $5$
  4. (C) longest
  5. (A) Yes
Section B — Short Answer (2 marks)
  1. $10$.
  2. $13$.
  3. $(\text{hyp})^2=(\text{base})^2+(\text{height})^2$.
  4. The hypotenuse.
Section C — Short Answer (3 marks)
  1. $15$.
  2. $15$.
  3. $25$.
  4. Yes.
Section D — Long Answer (5 marks)
  1. $29$ cm.
  2. Other leg $24$ cm; area $84$ cm$^2$.
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