Triangles on Same Base and Between Same Parallels
Triangles on Same Base and Between Same Parallels
Theorem: Triangles on the same base and between the same parallels are equal in area. Given Two triangles ABC and PBC on the same base BC and between the same parallel line BC and AP. To prove Construction Through Proof we have, and,
Similarly, Now, paralllograms
We know that the diagonals of a parallelogram divides it into two triangles of equal area.
and, Now,
Hence,
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ILLUSTRATION: The side AB of a parallelogram ABCD is produced to any point P. A line through A parallel to CP meets CB produced at Q then parallelogram PBQR is constructed. Show that ar( ABCD)= ar (PBQR)
Solution: ar ( Subtracting common ar (ABQ) from both sides we get ar ( ar ( We know that the diagonal divides a parallelogram in two congruent triangles From Eq (1), (2) and (3) we get ar( ABCD)= ar (PBQR) Hence Proved. |  |
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| Right Option : B | |||||
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| Right Option : C | |||||
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| Right Option : C | |||||
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