Home
Class 9
MATHS
P and Q are any two points lying on the...

`P` and `Q` are any two points lying on the sides `DC` and `AD` respectively of a parallelogram `ABCD`. Show that `a r\ (A P B)\ =\ a r\ (B Q C)`.

Text Solution

Verified by Experts

Draw `PM bot AB and QN bot BC`
`ar(DeltaAPB) = (1)/(2) xx (AB xx PM) = (1)/(2) xx ar (||gm ABCD)`....(1)
`ar(DeltaBQC) = (1)/(2) xx (BC xx QN) = (1)/(2) xx ar (||gm ABCD)`...(2)
`:.` From (1) and (2), we get
`ar(DeltaAPB) = ar(DeltaBQC)`
Promotional Banner

Topper's Solved these Questions

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise|34 Videos

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (very Short Answer Questions)|10 Videos

  • AREA OF PARALLELOGRAMS AND TRIANGLES

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (long Answer Question)|5 Videos

  • CIRCLE

    NAGEEN PRAKASHAN ENGLISH|Exercise Revision Exercise (long Answer Questions )|5 Videos

Similar Questions

Explore conceptually related problems

p\ A N D\ q are any two points lying on the sides D C\ a n d\ A D respectively of a parallelogram A B C Ddot\ Show that a r( A P B)=a r\ ( B Q C)dot

P and Q are points on the sides C A and C B respectively of A B C , right-angled at C . Prove that A Q^2+B P^2=A B^2+P Q^2 .

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r(triangle A D F)=a r( triangle D C E) .

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( /_\A D F)=a r( /_\D C E).

In Figure, P is a point in the interior of a parallelogram A B C Ddot Show that a r( A P B)+a r( P C D)=1/2a r\ (|""|^(gm)A B C D) a r\ ( A P D)+a r\ ( P B C)=a r\ ( A P B)+a r( P C D)

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR ABC D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed. Show that a r\ (A B C D)\ =\ a r\ (P B Q R) .

In Figure, P is a point in the interior of a parallelogram A B C D . Show that a r( A P B)+a r( P C D)=1/2a r(^(gm)A B C D) a R(A P D)+a r( P B C)=a r( A P B)+a r( P C D)

In Figure, A P || B Q\ || C R . Prove that a r\ ( A Q C)=\ a r\ (P B R)

ABCD is a parallelogram. P and Q are the mid-points of sides AB and AD reapectively. Prove that area of triangle APQ= (1)/(8) of the area of parallelogram ABCD.