Question

Abcd is a parallelogram. Line segments ae and cf bisect angle a and angle c respectively.Show that ae is parallel to cf

Answer 1

Answer:

Given,

ABCD is a ||gm , linesegment AE and CF bisects <A and <C .

To proof,

AE || CF

Proof,

(1) <A = <C

=> 1/2 <A = 1/2 <C

=> <1 = <2

(2) AB||CD and CY is the transversal

So, <2=<3.

From equation (1) and (2) we have ,

=> <1 = <2

Transversal AB intersect AE and CF at A and F such that ,

=> <1 = <3

= AE||CF

Hence , proved !!