Points D (0,0), E (8,-2), and F (9,2) are three vertices of a quadrilateral What must be the coordinates of G if DE is parallel to FG and AG is parallel to EF ?
Answers
Answered by
0
Step-by-step explanation:
E,F,G and H are respectively the mid-points of the sides of a parallelogram ABCD.
To Prove:
ar(EFGH)=
2
1
ar(ABCD)
Construction:
H and F are joined.
Proof:
AD∥BC and AD=BC (Opposite sides of a parallelogram)
⇒
2
1
AD=
2
1
BC
Also,
AH∥BF and and DH∥CF
⇒AH=BF and DH=CF ∣ H and F are mid points
Thus,
ABFH and HFCD are parallelograms.
Now,
△EFH and ||gm ABFH lie on the same base FH and between the same parallel lines AB and HF.
∴ Area of EFH=
2
1
ar(ABFH) --- (i)
Also,
Area of GHF=
2
1
ar(HFCD) --- (ii)
Adding (i) and (ii),
Area of △EFH+ area of △GHF =
2
1
ar(ABFH)+
2
1
ar(HFCD)
⇒ Area of EFGH= Area of ABFH
⇒ar(EFGH)=
2
1
ar(ABCD)
Similar questions