Vidaara.orgClass 8 · Mathematics
CodeVID-M08-10-MED-01
Medians, Altitudes & Construction - 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.
A median joins a vertex to the ___ of the opposite side.
- A.endpoint
- B.midpoint
- C.third
- D.foot
2.
An altitude is ___ to the opposite side.
- A.parallel
- B.perpendicular
- C.equal
- D.tangent
3.
The medians meet at the:
- A.orthocentre
- B.centroid
- C.incentre
- D.circumcentre
4.
A triangle has how many medians?
- A.$1$
- B.$2$
- C.$3$
- D.$4$
5.
The centroid divides each median in ratio:
- A.$1:1$
- B.$2:1$
- C.$3:1$
- D.$1:2$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
How many medians does a triangle have?
7.
What angle does an altitude make with the base?
8.
Where do the medians meet?
9.
A median goes to the ___ of the opposite side.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
In what ratio does the centroid divide a median?
11.
How many altitudes does a triangle have?
12.
In an equilateral triangle, is the median also an altitude?
13.
What is the meeting point of the altitudes called?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Explain the difference between a median and an altitude, naming the special point each set passes through.
15.
List the steps to construct a triangle with sides $5$ cm, $6$ cm and $7$ cm (SSS).
Answer Key
Section A — Multiple Choice Questions
- (B) midpoint
- (B) perpendicular
- (B) centroid
- (C) $3$
- (B) $2:1$
Section B — Short Answer (2 marks)
- $3$.
- $90^\circ$.
- At the centroid.
- Midpoint.
Section C — Short Answer (3 marks)
- $2:1$.
- $3$.
- Yes.
- The orthocentre.
Section D — Long Answer (5 marks)
- A median joins a vertex to the midpoint of the opposite side; medians meet at the centroid ($2:1$). An altitude is the perpendicular from a vertex to the opposite side; altitudes meet at the orthocentre.
- Draw the base $7$ cm; from one end draw an arc of radius $5$ cm; from the other end an arc of radius $6$ cm; their intersection is the third vertex; join it to both ends.
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