Question

in a triangle abc D,E, F are midpoints of the sides ac ab bc respectively BE perpendicular AC Prove that angle EFG= angles EDF.

Answer 1

Step-by-step explanation:

this is the answer of this question

please mark me the brainliest

Answer 2

Answer:

1:4

Step-by-step

Since D and E are the mid-points of the sides BC and AB respectively of △ABC.

Therefore,

DE∣∣BA

⇒ DE∣∣F

Since D and F are mid-points of the sides BC and AB respectively of △ABC.

∴

From (i), and (ii), we conclude that AFDE is a parallelogram.

Similarly, BDEF is a parallelogram.

Now, in △DEF and △ABC, we have

∠FDE=∠A [Opposite angles of parallelogram AFDE)

and, ∠DEF=∠B [Opposite angles of parallelogram BDEF]

So, by AA-similarity criterion, we have

△DEf∼△ABC

⇒

ARE(△ABC)

Area(△DEF)

=

Hence, Area(△DEF):Area(△ABC)=1:4

Hence, Area(△DEF):Area(△ABC)=1:4