in a parallelogram prove that the segments connecting the mi

in a parallelogram prove that the segment\'s connecting the midpoints of opposite sides bisect each other

hint what are some of our favorite segments to draw in a quadrilateral

Solution

we h ave a quadrilateral ABCD with midpoints PQRS

draw PQ, QR, RS, SP.

draw diagonals AC and BD.

theorem : the line segment joining the modpoints of two sides of a triangle is parallel to and one-half the length of third side.

in triangle ABC : PQ is parallel to AC and PQ = 1/2 AC

In trianle ADC : RS is parallel to AC and RS = 1/2 AC

hence : PQ parallel to RS and PQ = RS

theorem: if two s ides of a quadrilateral are parallel and equal,the quadrilateral is a parallelogram.

Hence PQRS is a parallelogram.