In a rectangle ABCD, E, F, G, and H are the midpoints of the four sides, what kind of shape is represented by EFGH.
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Step by Step Explanation:
- The following figure shows the rectangle ABCD,
Let's assume the length and breadth of the rectangle ABCD be a and b respectively.
- In ΔGDH, DG = = ,
DH = = [Since, G and H are the midpoints of the sides CD and DA respectively.]
∠D = 90° [Since, ABCD is a rectangle.]
GH2 = DG2 + DH2 [By the pythagorean theorem.]
⇒ GH2 = ( )2 + ( )2
Similarly, HE2 = EF2 = FG2 = ( )2 + ( )2
and hence, HE2 = EF2 = FG2 = GH2,
or HE = EF = FG = GH
- We know that quadrilateral with all four sides equal is rhombus. Therefore, EFGH is a Rhombus.