Question

In the given figure, ABCD is a parallelogram, and line segments AE and FC bisect angles angles A and C respectively. Show that AE||FC​
Please answer step by step

Answer 1

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Given that,

ABCD is Parallelogram

Then.

∠A =∠C

⇒21∠A = 21∠C 

∴  ∠1=∠2  ...... (1)

AF is the bisector of ∠A and CF is the bisector of ∠C

Now,  

AB || DC and CF is intersect them.

∴ ∠2 = ∠ 3  ......  (2)

[Alternate angle are equal]

From (1) and (2) to

∠1 = ∠3

AE || CF 

Hence, proved.