Question

In fig.

(a) find AE + EC.

(b) find AC – EC.

(c) find BD – BE.

(d) What is BD – DE?

Answer 1

(a) In line segments AE and EC, point E is a common point
So, AE + EC = AC

(b) In part (a) we have proved that:
AE + EC = AC
$\Rightarrow$ AC – EC = AE

(c) For line segments BE and ED, point E is a common point.
So, BE + ED = BD
$\Rightarrow$ BE – BE = ED

(d) Also, BE = BE + ED
$\Rightarrow$ BD – DE = BE
($\because$ line segment ED = line segment DE)