Home
Class 9
MATHS
ABCD is a trapezium with A B|| D C. A l...

ABCD is a trapezium with `A B|| D C`. A line parallel to AC intersects AB at X and BC at Y. Prove that `a r\ (A D X)\ =\ a r\ (A C Y)`.

Text Solution

Verified by Experts

`ABCD` is a trapezium with `AB∥DC` and `XY∥AC`.
Join `YA`,`XC` and `XD`.
Triangles `ACX` and `ACY` have same base `AC` and are between same parallels `AC` and `XY`.
So, `ar(ACX)=ar(ACY)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

A B C D is a trapezium with A B||D C . A line parallel to A C intersects A B\ at X\ a n d\ B C at Ydot Prove that a r( A D X)=a r(\ A C Y)dot

A B C D is a trapezium with A B || D C . A line parallel to A C intersects A B at X and B C at Y . Prove that a r( triangle A D X)=a r(triangle A C Y) .

ABCD is a trapezium with AB parallel to DC. A line parallel to AC intersects AB at X and BC at Y. Prove that area of DeltaADX = area of DeltaACY .

ABCD is a trapezium with AB parallel to DC. A line parallel to AC intersects AB at X and BC at Y. Prove that area of DeltaADX = area of DeltaACY .

ABCD is a trapezium with AB////DC . A line parallel to AC intersects Ab at point M and BC at point N. Prove that : "area of" DeltaADM= "area of" DeltaACN .

In Figure, B C ||X Y ,B X||C A and A B|| YC Prove that: a r( A B X)=a r( A C Y)

A B C D is a parallelogram whose diagonals A C\ a n d\ B D intersect at O . A line through O intersects A B\ a t\ P\ a n d\ D C\ at Q . Prove that a r\ (\ /_\P O A)=\ a r\ (\ /_\Q O C) .

Diagonals A C\ a n d\ B D of a trapezium A B C D with A B||D C intersect each other at O . Prove that a r\ ( A O D)=\ a r\ ( B O C) .

A B C D is a trapezium in which AB is parallel to CD . The diagonals A C and B D intersect at O . Prove that (i) A O B ~ C O D (ii) If O A=6c m , O C=8c m , Find: (A r e a\ ( A O B))/(A r e a\ ( C O D)) (b) (A r e a\ ( A O D))/(A r e a\ ( C O D))

A B C D is a parallelogram in which B C is produced to E such that C E=B C. A E intersects C D\ at F . Prove that a r\ (\ A D F)=\ a r\ (\ E C F) . If the area of \ D F B=3\ c m^2, find the area of ABCD.