Proposed Problem

In the figure below ABCD is an equilic quadrilateral. Prove that the midpoints E, G, F, and H of the diagonals and the sides BC and AD always determine a rhombus EFGH.

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gogeometry.com/equilic/equilic_quadrilateral_03.htm

Level: High School, SAT Prep, College geometry

## Saturday, March 21, 2009

### Equilic Quadrilateral: Theorem 3. Rhombus

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60,
diagonal,
equilic quadrilateral,
rhombus

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1.BA//GH.......(mid point thm[m.p.t])

ReplyDelete2.BA//FE....(m.p.t)

3.hence Quadrilateral is //gm....(opp. side //)

4.FE=1/2BA.........(m.p.t)

5.FG=1/2CD......(m.p.t)

6.BA=CD.......(given)

7.HENCE,FE=FG.......(FROM 4,5,6)

8.As opp. sides // & adj. Sides congruent Quadrilateral is Rhombus...(define)

HENCE PROVED.