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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-22-CNV-01
Converse of Mid-Point Theorem - Assignment
Chapter: Midpoint Theorem
Topic: Converse of 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.
A line through one midpoint parallel to a second side bisects the:
  • A.first side
  • B.second side
  • C.third side
  • D.median
2.
A line through the midpoint of $AB$ parallel to $BC$ meets $AC$ at its:
  • A.endpoint
  • B.midpoint
  • C.third
  • D.quarter
3.
The converse helps locate the:
  • A.centroid
  • B.midpoint
  • C.area
  • D.angle
4.
The line in the converse is parallel to the:
  • A.first side
  • B.third side
  • C.median
  • D.altitude
5.
The bisected segment is divided 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.
State the converse of the midpoint theorem.
7.
A line through the midpoint of $AB$ parallel to $BC$ meets $AC$ where?
8.
What does the converse let you find?
9.
The line in the converse is parallel to which side?
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
In $\triangle ABC$, $D$ is the midpoint of $AB$ and $DE\parallel BC$ meets $AC$ at $E$. If $AC=10$, find $AE$.
11.
If $AE=4$ in such a configuration, find $AC$.
12.
The converse guarantees $E$ is the ___ of $AC$.
13.
If a line bisects two sides of a triangle, it is parallel to which side?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
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.
15.
A line through the midpoint of $AB$ parallel to $BC$ meets $AC$ at $E$ with $AE=6$ cm. Find $AC$.

Answer Key

Section A — Multiple Choice Questions
  1. (C) third side
  2. (B) midpoint
  3. (B) midpoint
  4. (B) third side
  5. (B) $1:1$
Section B — Short Answer (2 marks)
  1. A line through the midpoint of one side, parallel to a second side, bisects the third side.
  2. At the midpoint of $AC$.
  3. The midpoint of a side.
  4. The third side.
Section C — Short Answer (3 marks)
  1. $5$.
  2. $8$.
  3. Midpoint.
  4. The third side.
Section D — Long Answer (5 marks)
  1. By the converse, $E$ is the midpoint; $AE=7$ cm.
  2. $12$ cm.
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