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.
See more at:
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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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.