Vidaara.orgClass 9 · Mathematics
CodeVID-M09-08-MPT-01
Mid-Point Theorem - Assignment
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.
The midsegment is parallel to the:
- A.first side
- B.third side
- C.median
- D.altitude
3.
If the third side is $10$ cm, the midsegment is:
- A.$5$ cm
- B.$10$ cm
- C.$20$ cm
- D.$2.5$ cm
4.
The converse of the midpoint theorem says a line through one midpoint parallel to a side:
- A.is perpendicular
- B.bisects the third side
- C.equals it
- D.is a median
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.
If a side is $12$ cm, the midsegment parallel to it is:
7.
The midsegment is $7$ cm; the parallel side is:
8.
State the length relation in the midpoint theorem.
9.
The midsegment is parallel to which side?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
In $\triangle ABC$, $D$ and $E$ are midpoints of $AB$ and $AC$; if $BC=14$, find $DE$.
11.
If the midsegment $DE=9$, find $BC$.
12.
State the converse of the midpoint theorem.
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 $\triangle ABC$, $D,E,F$ are midpoints of $BC,CA,AB$. State the result about the four triangles formed.
15.
A triangle has sides $8,10,12$ cm. Find the perimeter of the triangle formed by joining the midpoints.
Answer Key
Section A — Multiple Choice Questions
- (B) half
- (B) third side
- (A) $5$ cm
- (B) bisects the third side
- (B) $1:1$
Section B — Short Answer (2 marks)
- $6$ cm.
- $14$ cm.
- The midsegment is half the third side.
- The third side.
Section C — Short Answer (3 marks)
- $7$.
- $18$.
- A line through the midpoint of one side, parallel to a second side, bisects the third side.
- $4$.
Section D — Long Answer (5 marks)
- They are four congruent triangles, each similar to $\triangle ABC$ in ratio $1:2$.
- $15$ cm (sides $4,5,6$).
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