Q6 of 13 Page 106

In □ABC, the line through a point P on BC, parallel to AC meets AB at Q. The line through Q, parallel to AP, meets BC at R.


Prove that

Here AB, CD are parallel, then draw a line parallel to AB or CD through P.



Then,


We know that ,


Any three parallel lines will cut any two lines into pieces whose lengths are in the same ratio.


Therefore, if we consider QR, AP, line through B parallel to QR, then it divides the BA and BP in the same ratio.


----1



Similarly, if we consider QR,AP, line through B parallel to QR, then it divides the BA and BP in the same ratio.


--------2


From 1 & 2, we have,



More from this chapter

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3

In the parallelogram ABCD, the line drawn through a point P on AB, parallel to BC, meets AC at Q. The line through Q, parallel to AB meets AD at R.


i) Prove that


ii) Prove that

4

In the picture below, two vertices of a parallelogram are joined to the midpoints of two sides.


Prove that these line divide the diagonal in the picture into three equal parts.

 5

Prove that the quadrilateral formed by joining the midpoints of a quadrilateral is a parallelogram. What if the original quadrilateral is a rectangle? What if it is a square?

 7

AB and CD are parallel lines in the picture.


Prove that AP × PC = BP × PD