Question

The side AC of a triangle ABC is produced
1
to point E so that CE = AC. D is the mid-
2
point of BC and ED produced meets AB at f lines through D and C are drawn parallel to AB which meet AC at point P and EF at point are. prove that:.
(i) 3DF=EF
(ii) 4CR=AB
​

Answer 1

Answer:

Given that D is the midpoint of BC and DP is parallel to AB, therefore P is the midpoint of AC

PD=

2

1

AB

From the triangle PED we have PD∥CR and C is the midpoint of PE therefore CR=

2

1

PD

PD=

2

1

AB

2

1

PD=

4

1

AB

CR=

4

1

AB

4CR=AB