← Back to topic
Vidaara.orgClass 9 · Mathematics
CodeVID-M09-09-SMB-01
Shapes on the Same Base - Assignment
Chapter: Areas of Parallelograms and Triangles
Topic: Geometric Relationships Between Shapes on the Same Base
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.
Parallelograms on the same base/parallels are equal in:
  • A.perimeter
  • B.area
  • C.angle
  • D.diagonal
2.
Triangles on the same base/parallels are equal in:
  • A.perimeter
  • B.area
  • C.angle
  • D.height ratio
3.
A triangle on the same base/parallels as a parallelogram is ___ the parallelogram.
  • A.equal to
  • B.half
  • C.twice
  • D.a quarter
4.
"Between the same parallels" means equal:
  • A.base
  • B.height
  • C.area
  • D.perimeter
5.
A median divides a triangle into two triangles of:
  • A.unequal area
  • B.equal area
  • C.equal perimeter
  • D.right angles
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Two triangles on the same base/parallels have areas in what ratio?
7.
Two parallelograms on the same base/parallels have areas:
8.
What does "between the same parallels" guarantee?
9.
A triangle on the same base/parallels as a parallelogram of area $40$ has area:
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Triangles $ABC$ and $DBC$ are on the same base $BC$ between the same parallels; if area $ABC=25$, find area $DBC$.
11.
A median of a triangle divides it into two triangles of what areas?
12.
Into how many equal-area triangles do the diagonals of a parallelogram divide it?
13.
A diagonal splits a parallelogram of area $36$ into two triangles. Find each triangle's area.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
State and justify: a median of a triangle divides it into two triangles of equal area.
15.
Show that the diagonals of a parallelogram divide it into four triangles of equal area.

Answer Key

Section A — Multiple Choice Questions
  1. (B) area
  2. (B) area
  3. (B) half
  4. (B) height
  5. (B) equal area
Section B — Short Answer (2 marks)
  1. $1:1$.
  2. Equal.
  3. Equal heights.
  4. $20$.
Section C — Short Answer (3 marks)
  1. $25$.
  2. Equal areas.
  3. $4$.
  4. $18$.
Section D — Long Answer (5 marks)
  1. Equal areas (same base length and same height from the opposite vertex).
  2. Four triangles of equal area.
Generated by Vidaara.org · Assignment VID-M09-09-SMB-01 · vidaara.org