Question

HI FRIENDS..... ☺ ✨
The question is....

Show that the line segment with joins the midpoints of the oblique sides of trapezium is parallel to the parallel sides.

Please tell me how (In the picture) It is written DC || EF, just after saying PD/DE = PC/CF
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Answer 1

Here is your answer
DC IS PARALLEL TO EF
BECAUSE BY CONVERSE OF THALE's theorem we know that if a line intersects any two side of a ∆ in the same ratio then the line is parallel to the third side.

Here, DC intersects PE AND PF IN THE SAME RATIO
SO,DC is parallel to EF

HOPE IT IS USEFUL