Prove Exterior Angle Bisector Property in Triangle ABC & Point D

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SUMMARY

The discussion focuses on proving the Exterior Angle Bisector Property in triangle ABC, specifically that if point D lies on line AB and CD bisects the exterior angle at C, then the ratio BD/AD equals BC/AC. Participants emphasize the importance of constructing a similar triangle to facilitate the proof. A suggested approach involves drawing a line through point D that is parallel to side BC, which aids in establishing the necessary relationships between the triangles.

PREREQUISITES
  • Understanding of triangle properties and angle bisectors
  • Familiarity with similar triangles and their properties
  • Knowledge of basic geometric constructions
  • Ability to apply the Exterior Angle Theorem
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  • Study the properties of similar triangles in geometry
  • Learn about the Exterior Angle Theorem and its applications
  • Practice geometric constructions involving angle bisectors
  • Explore proofs related to triangle ratios and their applications
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Students studying geometry, mathematics educators, and anyone interested in understanding triangle properties and proofs related to angle bisectors.

Chemistry101
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1. Prove the property of exterior angle bisectors discussed in class. Given triangle ABC and point D on line AB such that CD bisects the exterior angle at C, then BD/AD=BC/AC.

The only thing I can compute about this problem is the Property of Exterior Angle, but I don't know how to apply it to the problem.

Exterior Angle is the angle between any side of a shape, and a line extended from the next side. <-- That's is all I understand.

Help on where to start this problem out with.

Thanks.
 
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Chemistry101 said:
1. Prove the property of exterior angle bisectors discussed in class. Given triangle ABC and point D on line AB such that CD bisects the exterior angle at C, then BD/AD=BC/AC.

Hi Chemistry101! :smile:

You need to find (ie make) a similar triangle somewhere.

Hint: draw a line through D parallel to BC :smile:
 

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