Which quadrilateral is formed by joining the mid points of the adjacent sides of a rectangle is a rhombus? In the figure below given that EFGH is a rectangle and P, Q, R, S are mid-points of sides EF, FG, GH & HE respectively. Justify.
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Step-by-step explanation:
In ΔABD, EH ll BD (Mid-point theorem)
In ΔCBD, FG ll BD (Mid-point theorem)
In ΔACD, GH ll AC (Mid-point theorem)
In ΔABC, EF ll AC (Mid-point theorem)
Since AC is perpendicular to BD, therefore adjacent sides of quadrilateral EFGH are perpendicular => Rectangle
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Answer:
rhombus
Step-by-step explanation:
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