Prove Exterior Angle Bisector Property in Triangle ABC & Point D

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In summary, the property of exterior angle bisectors was discussed in class. It states that for a triangle ABC and point D on line AB where CD bisects the exterior angle at C, the ratio of BD to AD is equal to the ratio of BC to AC. To solve this problem, one must create a similar triangle by drawing a line through D parallel to BC.
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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:
 

1. What is the exterior angle bisector property in a triangle?

The exterior angle bisector property states that the exterior angle formed by extending one side of a triangle is equal to the sum of the two interior angles that are opposite to the extended side.

2. How can I prove the exterior angle bisector property in a triangle?

To prove the exterior angle bisector property in a triangle, you can use the Angle Sum Theorem and the Exterior Angle Theorem. Let the triangle be ABC and the exterior angle be ACD. Then, using the Angle Sum Theorem, we know that m∠ACB + m∠BCA + m∠BAC = 180°. Since m∠ACD + m∠BCA = m∠ACB, we can substitute this into the equation and solve for m∠ACD to show that it is equal to m∠BAC + m∠BCA.

3. What is the importance of the exterior angle bisector property in a triangle?

The exterior angle bisector property is important because it helps us understand the relationship between the exterior angle and the interior angles of a triangle. It also allows us to solve for unknown angles and sides in a triangle using various geometric theorems and formulas.

4. Can the exterior angle bisector property be applied to any triangle?

Yes, the exterior angle bisector property can be applied to any triangle. It is a fundamental property of triangles and is applicable to all types of triangles, including equilateral, isosceles, and scalene triangles.

5. How is the exterior angle bisector property related to the angle bisector theorem?

The exterior angle bisector property is closely related to the angle bisector theorem. This theorem states that the angle bisector of an angle in a triangle divides the opposite side in the same ratio as the other two sides. The exterior angle bisector property can be seen as an extension of this theorem, where the exterior angle bisector divides the exterior angle into two angles that are equal to the angles formed by the angle bisector on the opposite sides.

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