Answer :

We have,


Given:


There are more than 1 parallelogram, and their bases can be taken as common and they are between same parallels.


To Prove:


These parallelograms whose bases are same and are between the same parallel sides have equal area.


Proof:


Let ABCD and ABFE be two parallelograms on the same base AB and between same parallel lines AB and DF.


Here,


AB DC and AE BF


We can represent area of parallelogram ABCD as,


…(i)


Now, area of parallelogram ABFE can be represented as,


Area of parallelogram ABFE



[ in right-angled ∆ADE, ]


Area of parallelogram ABFE


[ , where k is scalar; is parallel to and hence ]




[ a scalar term can be taken out of a vector product]



[ ]


Area of parallelogram ABFE …(ii)


From equation (i) and (ii), we can conclude that


Area of parallelogram ABCD = Area of parallelogram ABFE


Thus, parallelogram on same base and between same parallels are equal in area.


Hence, proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Find the angle beMathematics - Board Papers

If two vectors <sMathematics - Board Papers

If <span lang="ENMathematics - Exemplar

Show that area ofMathematics - Exemplar

Find the equationMathematics - Board Papers

Using vectors, fiMathematics - Board Papers

Find the angle beMathematics - Board Papers

Find the positionMathematics - Board Papers

<span lang="EN-USMathematics - Board Papers

If vectors <span Mathematics - Board Papers