Question

In the diagram, BC is parallel to EG, AC = EG = 15 cm, BC = CG, CD = 5 cm and
FG = 9 cm.
(i) Show that ABC and ECG are congruent.
(ii) Show that ACD and EFD are similar.
(iii) Find the length of DF.​
I will mark the first answer brainliest

Answer 1

Step-by-step explanation:

1) BC= CG (given)

angle BCA = angle FGC (corresponding angels, since BC parallel to FC)

CA = GE(given)

so by sas congruence both triangles are congruent

2)

angle FDE =angle CDA (vertically opposite angles)

angle FED = angle DAC (from ABC and ECG congruent triangles)

so by aa similarity both triangles are similar

3)

(CD/FD)= (AC/EF) by cpct

5/FD = (15/6)

FD = 30/15=2

SO FD =2