In a triangle \ A B C , If L\ a n d\ M a...

In a `triangle \ A B C ,` If `L\ a n d\ M` are points on `A B\ a n d\ A C` respectively such that `L M || B C`. Prove that: `a r\ (triangle \ L O B)=a r\ (triangle \ M O C)`

Topper's Solved these Questions

ALGEBRAIC IDENTITIES
RD SHARMA ENGLISH|Exercise All Questions|247 Videos
CIRCLE
RD SHARMA ENGLISH|Exercise All Questions|306 Videos

Similar Questions

Explore conceptually related problems

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ L O B)=a r\ (\ M O C) .

In a \ /_\A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ /_\L C M)=a r\ (/_\ L B M)

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B C . Prove that: a r\ (\ A B M)=a r\ (\ A C L) .

In a \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C respectively such that L M || B Cdot Prove that: a r\ (\ L B C)=\ a r\ (\ M B C)

In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A P . Prove that: a r\ ( triangle P B Q)=\ a r\ (triangle \ A R C)

In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A P . Prove that: a r\ (triangle \ P R Q)=1/2a r\ (triangle \ A R C) .

In triangle A B C ,\ P\ a n d\ Q are respectively the mid-points of A B\ a n d\ B C and R is the mid-point of A P . Prove that: a r\ ( triangle R Q C)=3/8\ a r\ (triangle \ A B C) .

A B C D is a parallelogram. L\ a n d\ M are points on A B\ a n d\ D C respectively and A L=C M . Prove that L M\ a n d\ B D bisect each other.

In figure, A B C D is a trapezium in which A B||C D . Prove that: a r( triangle A O D)=a r( triangle B O C) .

If A D is a median of a triangle A B C ,\ then prove that triangles A D B\ a n d\ A D C are equal in area. If G is the mid-point of median A D , prove that a r\ (triangle B G C)=2\a r\ (triangle \ A G C) .

RD SHARMA ENGLISH-AREA OF PARALLELOGRAMS AND TRIANGLES-All Questions

A B C D is a parallelogram, G is the point on A B such that A G=2\...
Text Solution
|
The side A B of a parallelogram A B C D is produced to any point Pdot ...
Text Solution
|
In a triangle \ A B C , If L\ a n d\ M are points on A B\ a n d\ A C...
Text Solution
|
D is the mid-point of side B C of triangle A B C and E is the mid-poi...
Text Solution
|
In Fig. 9.30, D and E are two points on BC such that B D=D E=E C . S...
Text Solution
|
A villager Itwari has a plot of land of the shape of a quadrilateral...
Text Solution
|
In parallelogram A B C D ,A B=10c m. The altitudes corresponding to th...
Text Solution
|
D, E, F are the mid points of side AB, BC, AC prove that BDEF is a pa...
Text Solution
|
If the medians of a triangle A B C intersect at G , show that a r( tr...
Text Solution
|
Prove that the area of an equilateral triangle is equal to (sqrt(3))...
Text Solution
|
In a parallelogram A B C D ,E ,F are any two points on the sides A B a...
Text Solution
|
The diagonals of a parallelogram A B C D intersect at Odot A line thro...
Text Solution
|
Show that the segment joining the mid-points of a pair of opposite s...
Text Solution
|
Diagonals A C and B D of a trapezium A B C D with A B || C D intersect...
Text Solution
|
In Figure, A B C D is a quadrilateral and B E || A C and also B E meet...
Text Solution
|
If a triangle and a parallelogram are on the same base and between the...
Text Solution
|
In Figure, A B C D E is a pentagon. A line through B parallel to A C m...
Text Solution
|
Prove that The area of a parallelogram is the product of its base and...
Text Solution
|
Prove that Parallelograms on the same base and between the same para...
Text Solution
|
Prove that A diagonal of a parallelogram divides it into two triangl...
Text Solution
|