1) AD is the median of the triangle ABC. E is any point on AD. Show that ar(triangle BED) = ar(triangle CED).

2)ABCD is a parallelogram BA is produced to E such that AE = AD. ED is produced to meet BC produced at F. Show that CD = CF

Please help me with the above questions

Thank You

(1)

Given that: AD is a median of  and E is any point on AD

To Prove:

Proof: 

Since, AD is the median of

So,

Also, ED is the median of ,

So,

(2)

Given that: ABCD is a parallelogram, BA is produced to E such that AE = AD and ED produced meets BC produced in F.

To Prove: CD = CF

Proof:

In ΔAED,

AE = AD (Given)

∴ ∠ADE = ∠AED  ..... (1) (In a triangle, equal sides have equal angles opposite to them)

AB || CD and EF is the transversal,

∴ ∠AED = ∠CDF  ...... (2) (Corresponding angles)

AD || BC and EF is the transversal,

∴ ∠ADE = ∠CFD  ..... (3) (Corresponding angles)

From (1), (2) and (3), we get

∠CDF = ∠CFD

In ΔCDF,

∠CDF = ∠CFD

So,

CF = CD (In a triangle, equal sides have equal angles opposite to them)