Prove: Angle Bisector Theorem

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Let's draw parallel lines to generate equal angles and use the resulting similar triangles to prove the angle bisector theorem.

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Комментарии
Автор

3:28 I got lost here, so just so no one else does, angle CAD is equal to CED because it's also equal to BAD! That's the theorem itself, the bisector of angle CAB makes CAD = BAD

wetsuitcandy
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Wow great sir, the way u taught will remain in brain 4 ever, thank u very much

dancingbaba
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Angke BAD=DAC (bissector) (1)
In triangle BAD:
SinBAD/x =sin(BDA)/a (2)
In triangle DAC:
Sin(DAC)/y=sin(ADC)/b
=sin(BDA) (3) :ADC=pi-BDA.
(1), (2) and (3) give: x/a=y/b.

touhami
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For me proof using law of sines is clear

holyshit
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Jay Hanuman Jay Hanuman Radhe Krishna Radhe Krishna

radhekrishna
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Thank you! The proof was very clear. Btw, are you from S. Korea?

qwertyuiop
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Can you prove the length of AD is equal to sqrt(a*b-x*y)?

RichardChen
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You can also prove this by using basic proportional theorem

ps-mxdq
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Hare Krishna Hare Krishna Krishna Krishna Hare Hare
Hare Ram Hare Ram Ram Ram Hare Hare

mathsclassesbyomsir
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It's immediate with law of sines, using BAD = DAC and sin(BDA) = sin(ADC).

michellauzon