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Vidaara.orgClass 9 · Mathematics
CodeVID-M9-23-CT
Pythagoras Theorem — Full Chapter Test
Chapter: Pythagoras Theorem
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • 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.
If $a^2+b^2=c^2$, the angle opposite $c$ is:
  • A.$60^\circ$
  • B.$90^\circ$
  • C.$45^\circ$
  • D.$120^\circ$
3.
The diagonal of a rectangle $l\times b$ is:
  • A.$l+b$
  • B.$\sqrt{l^2+b^2}$
  • C.$lb$
  • D.$2(l+b)$
4.
The side opposite the right angle is the:
  • A.base
  • B.height
  • C.hypotenuse
  • D.median
5.
The converse tests whether a triangle is:
  • A.equilateral
  • B.right-angled
  • C.isosceles
  • D.scalene
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the hypotenuse of a right triangle with legs $6$ and $8$.
7.
Is $5,12,13$ a right triangle?
8.
Find the diagonal of a rectangle $6$ by $8$.
9.
Find the hypotenuse with legs $5$ and $12$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Find the hypotenuse with legs $9$ and $12$.
11.
Check whether $7,24,25$ form a right triangle.
12.
Find the diagonal of a rectangle $12$ cm by $16$ cm.
13.
One leg is $8$, hypotenuse $17$; find the other leg.
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.
Determine whether the triangle with sides $9,40,41$ is right-angled, and name the hypotenuse.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $(\text{base})^2+(\text{height})^2$
  2. (B) $90^\circ$
  3. (B) $\sqrt{l^2+b^2}$
  4. (C) hypotenuse
  5. (B) right-angled
Section B — Short Answer (2 marks)
  1. $10$.
  2. Yes.
  3. $10$.
  4. $13$.
Section C — Short Answer (3 marks)
  1. $15$.
  2. Yes ($49+576=625$).
  3. $20$ cm.
  4. $15$.
Section D — Long Answer (5 marks)
  1. $29$ cm.
  2. Right-angled; hypotenuse $41$ ($81+1600=1681$).
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