In figure, P is a point in the interior of a parallelogram ABCD. Show that
[Hint: Through P, draw a line parallel to AB.]
ABCD is a parallelogram and P is a point present in parallelogram ABCD.
We need to show that
Construction: Draw a line EF passing through P which is parallel to AB. (1)
We also have (Because ABCD is a parallelogram) (2)
From (1) and (2), we can say that ABFE is a parallelogram.
(A quadrilateral is a parallelogram if both the pairs of opposite sides are parallel)
Similarly, we can prove that EFCD is a parallelogram.
So, we can notice that and parallelogram ABFE are on the same base AB and between the same parallels AB and EF.
Similarly, and parallelogram EFCD are on the same base CD and between the same parallels EF and CD.
Adding (3) and (4), we get
We have already proved above that
Similarly, by drawing a line through P which is parallel to AD, we can show that
From (5) and (6), we can say that