MEDIUM
9th West Bengal Board
IMPORTANT
Earn 100

Prove that the area of a rhombus is half the area of the rectangle produced by the diagonals of the rhombus .

Important Questions on Theorems on Areas

EASY
9th West Bengal Board
IMPORTANT
MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 9
D, E and F are the midpoints of the sides AB, BC and CA of the△ABC. Prove that △DEF=14△ABC.
MEDIUM
9th West Bengal Board
IMPORTANT
MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 10
If E be the midpoints of the median AD of △ABC, then prove that △BED=14△ABC.
EASY
9th West Bengal Board
IMPORTANT
MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 11
Prove that two diagonals of a parallelogram divides it into four triangles of equal area.
EASY
9th West Bengal Board
IMPORTANT
MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 12
P is any point on AD, the median of △ABC. Prove that △ABP=△ACP
EASY
9th West Bengal Board
IMPORTANT
MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 15
The diagonals AC and BD of a quadrilateral ABCD intersects each other at O such that △AOD=△BOC. Prove that ABCD is a trapezium.
EASY
9th West Bengal Board
IMPORTANT
MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 18
P and Q are the midpoints of the sides AB and CD of the parallelogram ABCD. Prove that PBQD is a parallelogram.
MEDIUM
9th West Bengal Board
IMPORTANT
MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 19
On the outside of the equilateral triangle ABC and in the angular region ∠ABC, O is a point. OP, OQ and OR are the perpendiculars drawn from O to the sides AB, BC, AC respectively. Prove that height of the triangle=OP+OQ-OR.
MEDIUM
9th West Bengal Board
IMPORTANT
MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 21
Prove that sum of the perpendiculars drawn from any interior point of an equilateral triangle to its sides equal to its height.