In the triangle ABC, point D is on the edge AC, DB = BC, point E is the midpoint of CD, point F is the midpoint of AB, passing through point a as Ag parallel EF, The extension line of intersection be is at point g. try to explain that the triangle Abe is equal to the triangle age

In the triangle ABC, point D is on the edge AC, DB = BC, point E is the midpoint of CD, point F is the midpoint of AB, passing through point a as Ag parallel EF, The extension line of intersection be is at point g. try to explain that the triangle Abe is equal to the triangle age

prove:
BD = BC, C is the midpoint of CD
Be is perpendicular to CD
∠AEB=90°
F is the midpoint of AB (F is the center of the triangle Abe circumscribed circle, AB is the diameter, AF, EF, BF are the radius)
Then BF = EF = AF
The triangle bef is an isosceles triangle
∠EBF=∠BEF
AG//EF
Then ∠ g = ∠ bef
There is ∠ EBF = ∠ G
That is, Abe = G
∠AEB=∠AGE=90°
AE is the common edge
So the triangle Abe is equal to the triangle age

In △ ABC, bisectors of ∠ B and ∠ C intersect at point O, passing through o to make ef ‖ BC intersect AB and AC at e and F

Certification:
∵ Bo bisection ∠ ABC
∴∠ABO＝∠CBO
∵EF∥BC
∴∠EOB＝∠CBO
∴∠ABO＝∠EOB
∴BE＝EO
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