Question

EFGH is a trapezium in which EF || HG, FH is a diagonal and P is the

mid-point of EH. A line drawn through P parallel to EF intersecting FG

at Q. Show that Q is the mid-point of FG.​

Answer 1

Answer:

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Answer 2

Answer:

The converse of the midpoint theorem declares that ” if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side”.

Step-by-step explanation:

According to the converse of the midpoint theorem,

if a line is drawn through the midpoint of one side of a triangle, and parallel to the other side, it bisects the third side.

In ΔEFH

P is the midpoint of EH

Also, PT║EF (given)

⇒T is the midpoint of FH (converse of midpoint theorem)

Since EF║HG and PQ║EF

⇒HG║PQ

In ΔFGH

Q exists at the midpoint of FG

Furthermore, TQ║HG

⇒ Q exists the midpoint of FG (converse of midpoint theorem)

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