Question

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

Answer 1

Answer:

EFGH is a parallelogram

Step-by-step explanation:

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively

lets join AC

Then ΔDAC & ΔAHG

AH = DA/2  ,  AG = CD/2  ∠A is common

=> ΔDAC ≅ ΔAHG

& GH ║ AC  & GH = AC/2

Similarly EF ║AC & EF = AC/2

Hence GH ║EF  & GH = EF = AC/2

Similarly we can show that

FG ║ BD ║ EH   & FG = EH = BD/2

Hence opposite sides are parallel & equal

=> EFGH is a parallelogram.