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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-22-MPT-01
The Mid-Point Theorem - Assignment
Chapter: Midpoint Theorem
Topic: The Mid-Point 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.
The midsegment equals ___ of the third side.
  • A.the whole
  • B.half
  • C.twice
  • D.a third
2.
If the third side is $12$, the midsegment is:
  • A.$6$
  • B.$12$
  • C.$24$
  • D.$3$
3.
The three midsegments make how many congruent triangles?
  • A.$2$
  • B.$3$
  • C.$4$
  • D.$6$
4.
The midsegment is parallel to the:
  • A.first side
  • B.third side
  • C.median
  • D.altitude
5.
Midpoints divide a side in ratio:
  • A.$1:2$
  • B.$1:1$
  • C.$2:1$
  • D.$3:1$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
In $\triangle ABC$, $D,E$ are midpoints of $AB,AC$; if $BC=16$, find $DE$.
7.
If $DE=11$, find $BC$.
8.
State the length part of the midpoint theorem.
9.
The midsegment is parallel to which side?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
In $\triangle PQR$, the midsegment parallel to $QR$ is $9$. Find $QR$.
11.
A triangle has sides $10,12,14$. Find the perimeter of its medial triangle.
12.
In $\triangle ABC$, $D,E$ are midpoints; if $DE=6.5$, find $BC$.
13.
Into how many congruent triangles do the three midsegments divide a triangle?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
In $\triangle ABC$, $D$ and $E$ are midpoints of $AB$ and $AC$. If $BC=18$ cm, find $DE$ and state its relation to $BC$.
15.
Find the perimeter of the medial triangle of a triangle with sides $14,16,18$ cm.

Answer Key

Section A — Multiple Choice Questions
  1. (B) half
  2. (A) $6$
  3. (C) $4$
  4. (B) third side
  5. (B) $1:1$
Section B — Short Answer (2 marks)
  1. $8$.
  2. $22$.
  3. The midsegment is half the third side.
  4. The third side.
Section C — Short Answer (3 marks)
  1. $18$.
  2. $18$.
  3. $13$.
  4. $4$.
Section D — Long Answer (5 marks)
  1. $DE=9$ cm; parallel to $BC$ and half its length.
  2. $24$ cm.
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