Question

please give me the proof​

Answer 1

AIM : TO PROVE CE Bisects <ACB.

Which means { <ACE ~ <ECB }

⚫️By intersecting parallel lines

we know that

⚫️<ACE ~ <CDB (AAA_property) or (scaled model) Equation 1

And

⚫️<ECB ~ <CBD ( Alternate interior angles)

Equation 2

⚫️Now consider ^BCD which is a isosceles triangle containing CB = CD.

⚫️we know that, on an isosceles triangle angles subtend by equal sides are equal.

⚫️=> <CBD ~ <CDB. ----> Equation3

⚫️=> From Equations 1, 2 and 3 we can conclude that.

⚫️< ACE ~ <CDB ~ <CBD ~ <ECB

⚫️=>> <ACE. ~ <ECB

Hope it helps, if you have any doubts feel free to comment below :)))