MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 8

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

A B, B C

and

C A

of the

△ A B C

. Prove that

△ D E F = \frac{1}{4} △ A B C

.

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

A D

of

△ A B C

, then prove that

△ B E D = \frac{1}{4} △ A B C

.

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

A D

, the median of

△ A B C

. Prove that

△ A B P = △ A C P

MEDIUM

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 13

P

is any point in the interior of the parallelogram

A B C D

. Prove that triangle

△ A P D + △ B P C = \frac{1}{2} ▱ A B C D

EASY

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 14

In the trapezium

A B C D

,

A B ∥ D C

and the diagonals

A C

and

B D

intersects each other at

O

. Prove that

△ A O D = △ B O C

.

EASY

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 15

The diagonals

A C

and

B D

of a quadrilateral

A B C D

intersects each other at

O

such that

△ A O D = △ B O C

. Prove that

A B C D

is a trapezium.

EASY

9th West Bengal Board

IMPORTANT

MATHEMATICS CLASS 9>Chapter 12 - Theorems on Areas>EXERCISE-3>Q 16

D

and

E

lie on the sides

A B

and

A C

of

△ A B C

such that

△ D B C = △ E B C

. Prove that

D E ∥ B C

.