ABCD is quadrilateral E, F, Grespectively. Prove that EFGH is a parall

1.	ABCD is quadrilateral E, F, Grespectively. Prove that EFGH is a parallelogram.and H are the midpoints of AB, BC, CD and DA
Answer» GIVEN, quad ABCD E,F,G,H are mid pointsTo Prove, EFGH is a parallelogram. Proof, Join AC and BD,In ∆ADC H is mid point of AD and G is mid point of DC.So by mid point theorem, HG \|\| AC and HG= AC/2.......(1) Similarly, EF \|\|AC and EF =AC/2........(2) By (1) & (2), HG \|\| EF and HG=AF We know,If in a quad opposite sides are equal and parallel then it is a parallelogram. Hence proved

ABCD is quadrilateral E, F, Grespectively. Prove that EFGH is a parallelogram.and H are the midpoints of AB, BC, CD and DA

Answer»

GIVEN, quad ABCD E,F,G,H are mid pointsTo Prove, EFGH is a parallelogram.

Proof,

Join AC and BD,In ∆ADC

H is mid point of AD and G is mid point of DC.So by mid point theorem,

HG || AC and HG= AC/2.......(1)

Similarly,

EF ||AC and EF =AC/2........(2)

By (1) & (2),

HG || EF and HG=AF

We know,If in a quad opposite sides are equal and parallel then it is a parallelogram.

Hence proved