Question

In this figure, AFC=EFC. Which statement must be true?

a) AD Perpendicular EB
b) EB Perpendicular CA
c) AD Perpendicular CE
d) CF Perpendicular AE

Answer 1

The answer is D, because AFC=EFC the CF is perpendicular to AE

Answer 2

The statement is true is CF Perpendicular AE .

Option (d) is correct.

Explanation:

As given

∠AFC = ∠EFC

Let us assume that the measure of ∠AFC be x.

Thus

∠AFC = ∠EFC = x

As

∠AFC + ∠EFC = 180° (By Linear pair property)

x + x = 180°

2x = 180°

`x = (180)/(2)`

x = 90°

Thus

∠AFC = ∠EFC = 90°

Therefore CF is perpendicular to AE .

Option (d) is correct.