Question

please answer by solving​

Answer 1

make my answer as a brain list

It is given that

ABCD is a kite in which BC=CD, AB=AD

E, F, G are midpoints of CD, BC and AB

To prove :

∠EFG=90

o

Construction :

Join AC and BD

Construct GH through G paralled to FE

Proof:

We know that,

Diagonals of a kite intersect at right angles

∴∠MON=90

o

...(1)

In △BCD

E and F are midpoints of CD and BC

⇒EF∥DB and EF=1/2DB...(2) [ By basic proportionality theorem ]

Now, EF∥DB⇒MF∥ON

Similarly, FG∥CA⇒FN∥MO

Therefore, in quadrilateral MFNO,

MF∥ON, FN∥MO and ∠MON=90

o

⇒MFNO is a square.

∴∠EFG=90

o