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In the triangle ABC, the angle ABC is 45 degrees. H is the intersection point of high AD and be. BH = AC, BH is perpendicular to AC
prove:
In triangle abd, angle abd = 45 degrees. ADB = 90 degrees
So the triangle abd is an isosceles right triangle
So BD = ad
Angle AEH = angle ACD = 90 degree angle eah = angle DAC
So the triangle eah is similar to the triangle DAC
So angle ahe = angle ACD
And angle Bhd = angle ahe (equal to vertex angle)
Angle BDH = angle ADC = 90 degrees
And BD = ad
So triangle BDH is equal to triangle ADC
So BH = AC
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