Question

the perpendicular from D on the side EF of
trigleDEF intersects Ef at N such that NF =3EN.
Prove that :-2(DF²-DE²) = EF²
​

Answer 1

Step-by-step explanation:

GIVEN:

NF + EN = EF

3EN + EN = EF

4EN = EF

PYTHAGORAS THEOREM:

DF^2 = DN^2 + NF^2

DE^2 = DN^2 + NE^2

DF^2 -DE^2 = NF^ - NE^2

= (NF + NE)*(NF - NE)

= (EF)*(2EN)

2*(DF^2 -DE^2) = EF*4EN

Therefore,

2*(DF² -DE ²) = EF²