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 parallelogramABCD. Show that `a r\ (A P B)\ =\ a r\ (B Q C)`.

Text Solution

AI Generated Solution

To prove that the area of triangle APB is equal to the area of triangle BQC in parallelogram ABCD, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Points**: - Let P be a point on side DC of parallelogram ABCD. - Let Q be a point on side AD of parallelogram ABCD. ...
Promotional Banner

Topper's Solved these Questions

  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    NCERT|Exercise EXERCISE 9.4|8 Videos
  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    NCERT|Exercise EXERCISE 9.1|1 Videos
  • AREAS OF PARALLELOGRAMS AND TRIANGLES

    NCERT|Exercise Solved Examples|4 Videos
  • CIRCLES

    NCERT|Exercise EXERCISE 10.2|2 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

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C 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.

In Fig. 4.238, S and T are points on the sides P Q and P R respectively of P Q R such that P T=2c m , T R=4c m and S T is parallel to Q R . Find the ratio of the areas of P S T and P Q R . (FIGURE)

In A 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 Pdot Prove that: a r\ ( P B Q)=\ a r\ (\ A R C)

P and Q are points on sides A B and A C respectively of A B C . If A P=3c m , P B=6c m , A Q=5c m and Q C=10 c m , show that B C=3\ P Q .

If AD and PM are medians of triangles ABC and PQR, respectively whereDeltaA B C DeltaP Q R , prove that (A B)/(P Q)=(A D)/(P M)

In a A B C , P and Q are point on the sides A B and A C respectively, such that P Q B C . If A P=2. 4 c m , A Q=2c m , Q C=3c m and B C=6c m , find A B and P Q .

In A 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 Pdot Prove that: a r\ ( R Q C)=3/8\ a r\ (\ A B C)

In A 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 Pdot Prove that: a r\ (\ P R Q)=1/2a r\ (\ A R C)

P and Q are respectively the mid-points of sides AB and BC of a triangle ABC and R is the mid-point of AP, show that (i) a r" "(P R Q)""=1/2a r""(A R C) (ii) a r" "(R Q C)""=3/8a r" "(A B C) (iii) a r" "(P B Q)" "=""a r" "(ARC)