Saturday, March 21, 2009

Equilic Quadrilateral: Theorem 3. Rhombus

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.

Equilic Quadrilateral: Theorem 3. Rhombus.

See more at:
gogeometry.com/equilic/equilic_quadrilateral_03.htm

Level: High School, SAT Prep, College geometry

1 comment:

  1. 1.BA//GH.......(mid point thm[m.p.t])
    2.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.

    ReplyDelete