Parallelograms on Same Base and Between Same Parallels
Parallelograms on Same Base and Between Same Parallels
Parallelograms On The Same (Equal) Base and Between The Same Parallels. Now we are going to discuss about the are of two parallelograms which lie on the same or equal base and between the same parallels.
Theorem 1 Parallelograms on the same base and between the same parallels are equal in area.
Given Two parallelograms ABCD and ABEF, which have same basae AB and which are between the same parallel lines AB and FC.
To prove Proof As ABDC is a parallelogram Similarly in Parallelogram ABEF From Eq. (1) and (2) We get DC = EF ...................(3) Subtracting FD from both sides in Eq (3) We get DC- FD = EF - FD In AC = BD [ Opposite side of the parallelogram ABDC] AF = BE [ Opposite side of the parallelogram ABEF] CF = DE [ From Equation(4)] So, Now, Adding Hence Proved |  |
Illustration: In the given figure, . If the ar (ABCD) = 25sq.m find the ar(DEFH)
Solution: In the given figure, we have AB || DC and AD || BC, Again,AD || BC Now ||gm ABCD and ||gm ADEG are on the same base AD and between the same parallels AD || BE
Again, AF || DE and EF || DC Now ||gm DEFH and ||gm ADEG are on the same base DE and between the same parallels DE || AF.
Hence ar(|| gm DEFH )= 25 sq. m. |  |
Two parallelograms are on equal bases and between the same parallels . The ratio of their areas is _____________________ | |||
| Right Option : B | |||
| View Explanation | |||
In the Given figure If area of parallelogram ABCD = 345
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| Right Option : A | |||
| View Explanation | |||
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| Right Option : C | |||||
| View Explanation | |||||
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