Can you solve the following question?
"Prove that the quadrilateral formed by joining the mid-points of the sides of a quadrilateral in order is a parallelogram."
Anonymous:
Do you have an idea about basic proportionality theorem?
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You need to use the midpoint theorem.
ABCD is a quadrilateral. P,Q,R,S are the midpoints of AB,BC,Cd,DA
PQ is parallel to AC
RS is parallel to AC
Therefore, PQ is parallel to RS
Similarly, PS is parallel to QR
Both the pairs of opposite sides are parallel and equal.Therefore, it is a parallelogram.
ABCD is a quadrilateral. P,Q,R,S are the midpoints of AB,BC,Cd,DA
PQ is parallel to AC
RS is parallel to AC
Therefore, PQ is parallel to RS
Similarly, PS is parallel to QR
Both the pairs of opposite sides are parallel and equal.Therefore, it is a parallelogram.
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