In the adjacent figure, ABCD is a parallelogram and line segments AE and CF bisect the angles A and C respectively. Show that AE||CF.

Asked by seemamehra1805 | 2nd Sep, 2020, 01:57: PM

Expert Answer:

ABCD is a parallelogram with AE and CF being the bisectors of angles A and C respectively.
As space ABCD space is space straight a space parallelogram
rightwards double arrow angle straight A equals angle straight C space space... space left parenthesis Opposite space angles space are space equal space in space straight a space vertical line vertical line gram right parenthesis
rightwards double arrow 1 half angle straight A equals 1 half angle straight C space
rightwards double arrow angle EAB equals angle ECF space... space left parenthesis straight i right parenthesis
Now comma space AB vertical line vertical line CD space and space CF space is space the space transversal
rightwards double arrow angle DCF equals angle BFC space space... space left parenthesis Alternate space angles right parenthesis
rightwards double arrow angle ECF equals angle BFC space... space left parenthesis ii right parenthesis
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
angle EAB equals angle BFC
They space form space straight a space pair space of space equal space corresponding space angles
rightwards double arrow AE vertical line vertical line CF

Answered by Renu Varma | 4th Sep, 2020, 02:23: PM