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Vidaara.orgClass 9 · Mathematics
CodeVID-M9-22-CT
Mid-point Theorem — Full Chapter Test
Chapter: Mid-point 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.
The midsegment equals ___ of the third side.
  • A.the whole
  • B.half
  • C.twice
  • D.a third
2.
A line through one midpoint parallel to a second side bisects the:
  • A.first side
  • B.second side
  • C.third side
  • D.median
3.
Equal intercepts on one transversal give equal intercepts on:
  • A.no other line
  • B.any other transversal
  • C.only vertical lines
  • D.the same line
4.
If the third side is $12$, the midsegment is:
  • A.$6$
  • B.$12$
  • C.$24$
  • D.$3$
5.
A line through the midpoint of $AB$ parallel to $BC$ meets $AC$ at its:
  • A.endpoint
  • B.midpoint
  • C.third
  • D.quarter
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.
State the converse of the midpoint theorem.
8.
State the intercept theorem.
9.
If $DE=11$, find $BC$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
In $\triangle PQR$, the midsegment parallel to $QR$ is $9$. Find $QR$.
11.
In $\triangle ABC$, $D$ is the midpoint of $AB$ and $DE\parallel BC$ meets $AC$ at $E$. If $AC=10$, find $AE$.
12.
Three parallel lines make intercepts of $3$ cm each on a transversal; on a second transversal one intercept is $4$ cm. Find the others.
13.
A triangle has sides $10,12,14$. Find the perimeter of its medial 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.
In $\triangle ABC$, $D$ is the midpoint of $AB$; a line through $D$ parallel to $BC$ meets $AC$ at $E$. State why $E$ is the midpoint and find $AE$ if $AC=14$ cm.

Answer Key

Section A — Multiple Choice Questions
  1. (B) half
  2. (C) third side
  3. (B) any other transversal
  4. (A) $6$
  5. (B) midpoint
Section B — Short Answer (2 marks)
  1. $8$.
  2. A line through the midpoint of one side, parallel to a second side, bisects the third side.
  3. Equal intercepts on one transversal give equal intercepts on any other transversal.
  4. $22$.
Section C — Short Answer (3 marks)
  1. $18$.
  2. $5$.
  3. $4$ cm each.
  4. $18$.
Section D — Long Answer (5 marks)
  1. $DE=9$ cm; parallel to $BC$ and half its length.
  2. By the converse, $E$ is the midpoint; $AE=7$ cm.
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