ABCD is a parallelogram E is the mid point of DC and through D , a line - Maths - Quadrilaterals

Question

ABCD is a parallelogram E is the mid point of DC and through D
, a line segment is drawn parallel to EB meet CB produced at G and
it cuts AB at F prove that (i)AD = half GC (ii)DG =2 EB

Priyanka Kedia · Accepted Answer

Given that: ABCD is a parallelogram and E is the mid-point of CD and EB||DG To Prove: AD = Â½ GC and DG = 2EB Proof: (1) In

, Since, E is the mid-point of CD and EB||DG Therefore by converse of mid-point theorem, B is the mid- point of CG Thus, CB = Â½ CG And ABCD is a parallelogram, so, AD=CB Thus, AD = Â½ GC (2) In

, E and B are the midpoints of CD and CG respectively Therefore by mid point theorem,

ABCD is a parallelogram E is the mid point of DC and through D , a line segment is drawn parallel to EB meet CB produced at G and it cuts AB at F. prove that (i)AD = half GC . (ii)DG =2 EB.