The vertices of the quadrilateral are the midpoints of the sides of the rhombus with diagonals of 8 cm

| April 6, 2021 | education

The vertices of the quadrilateral are the midpoints of the sides of the rhombus with diagonals of 8 cm and 14 cm. Determine the type of the quadrilateral and find its sides.

Since, by condition, the points K, M, H, P are the midpoints of the sides of the rhombus, the KM segment is the middle line of the triangle ABC. Since the length of the midline is equal to half the length of the base of the triangle parallel to the midline, then KM = AC / 2 = 14/2 = 7 cm.

The segment НР is the middle line of the triangle АСD, then НР = АС / 2 = 14/2 = 7 cm.

The segment KН is the middle line of the triangle ABD, then KН = BD / 2 = 8/2 = 4 cm.

Segment МР = middle line of triangle ВСD, then МР = ВD / 2 = 8/2 = 4 cm.

Since KM and HP are parallel to AC, then KM is parallel to HP, since KH and MR are parallel to BD, then KH is parallel to MР.

Since the diagonals of the rhombus intersect at right angles, and the sides of the CMРН quadrangle are parallel to the diagonals, then the angle between the sides of the CMРН is straight, then the CMРН  is a rectangle.

Answer: A quadrangle is a rectangle with sides 4 cm and 7 cm.



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