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CBSE Class 8 Answered

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 | 02 Sep, 2020, 01:57: PM
answered-by-expert 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 | 04 Sep, 2020, 02:23: PM

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