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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-23-CNV-01
Converse of Pythagoras - Assignment
Chapter: Pythagoras Theorem
Topic: Converse 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.
If $a^2+b^2=c^2$, the angle opposite $c$ is:
  • A.$60^\circ$
  • B.$90^\circ$
  • C.$45^\circ$
  • D.$120^\circ$
2.
The converse tests whether a triangle is:
  • A.equilateral
  • B.right-angled
  • C.isosceles
  • D.scalene
3.
For $6,8,10$, the triangle is:
  • A.acute
  • B.obtuse
  • C.right-angled
  • D.not a triangle
4.
The largest side is taken as the:
  • A.base
  • B.height
  • C.hypotenuse $c$
  • D.median
5.
If $a^2+b^2
  • A.right-angled
  • B.acute
  • C.obtuse
  • D.equilateral
    • Section B — Short Answer (2 marks) 4 × 2 = 8 marks
    6.
    Is $5,12,13$ a right triangle?
    7.
    Is $4,5,6$ a right triangle?
    8.
    State the converse of Pythagoras' theorem.
    9.
    Is $9,12,15$ right-angled?
    Section C — Short Answer (3 marks) 4 × 3 = 12 marks
    10.
    Check whether $7,24,25$ form a right triangle.
    11.
    Check whether $8,15,17$ form a right triangle.
    12.
    Check whether $10,24,26$ form a right triangle.
    13.
    Is $5,6,8$ right, acute or obtuse?
    Section D — Long Answer (5 marks) 2 × 5 = 10 marks
    14.
    Determine whether the triangle with sides $9,40,41$ is right-angled, and name the hypotenuse.
    15.
    The sides of a triangle are $11,60,61$. Show whether it is right-angled.

    Answer Key

    Section A — Multiple Choice Questions
    1. (B) $90^\circ$
    2. (B) right-angled
    3. (C) right-angled
    4. (C) hypotenuse $c$
    5. (C) obtuse
    Section B — Short Answer (2 marks)
    1. Yes.
    2. No ($16+25\ne36$).
    3. If $a^2+b^2=c^2$, the triangle is right-angled.
    4. Yes.
    Section C — Short Answer (3 marks)
    1. Yes ($49+576=625$).
    2. Yes.
    3. Yes ($100+576=676$).
    4. Obtuse ($25+36<64$).
    Section D — Long Answer (5 marks)
    1. Right-angled; hypotenuse $41$ ($81+1600=1681$).
    2. Yes; $121+3600=3721=61^2$.
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