ABCD is a quadrilateral in which a b equal to b c d e f g h are the midpoint - Maths - Coordinate Geometry

Question

ABCD is a quadrilateral in which a b equal to b c d e f g h are the
midpoint of Ab BC CD and ac respectively prove that fgh is a
rhombus

Neha Sethi · Accepted Answer

Given: ABCD is a quadrilateral in which AD=BC E,F,G and H are the mid points of AB,BD,CD and AC respectively
To show: EFGH is  rhombus
Now in △ACD , E and F are the mid points of  AB,AC respectively
⇒GH=12AD=12BC 
1  using BPT theoremSimilarly in △ABC,HE=12BC 
2  using BPT theoremNow consider △BCD ,G and F are the mid points of CD  and BD respectively  GF∥BC and GF=12BC  
3  using BPT theoremand similarly in △ABD,H and E are mid points of AC and AB respectivelyEF=12AD=12BC
4  using BPT theorem and AD=BCFrom 1,2,3 and 4EF=FG=GH=HASince all sides are equal so EFGH is rhombus

ABCD is a quadrilateral in which a b equal to b c d e f g h are the midpoint of Ab BC CD and ac respectively prove that fgh is a rhombus ABCD is a quadrilateral in which a b equal to b c d e f g h are the midpoint of Ab BC CD and ac respectively prove that fgh is a rhombus bC)-jY

ABCD is a quadrilateral in which a b equal to b c d e f g h are the midpoint of Ab BC CD and ac respectively prove that fgh is a rhombus

ABCD is a quadrilateral in which a b equal to b c d e f g h are the midpoint of Ab BC CD and ac respectively prove that fgh is a rhombus bC)-jY