# Please explain the exterior angle bisector theorem!!!

## Exterior Angle Bisector Theorem

Exterior angle bisector theorem : The external bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.

Given : A ΔABC, in which AD is the bisector of the exterior ∠A and intersects BC

produced in D.

Prove that : BD / CD = AB / AC

Construction : Draw CE || DA meeting AB in E.

 Statements Reasons 1) CE || DA 1) By construction 2) ∠1 = ∠3 2) Alternate interior angle 3) ∠2 = ∠4 3) Corresponding angle (CE ||DA and BK is a transversal 4) AD is a bisector of ∠A 4) Given 5) ∠1 = ∠2 5) Definition of angle bisector 6) ∠3 = ∠4 6) Transitivity (from 2 and 4) 7) AE = AC 7) If angles are equal then side opposite to them are also equal 8) BD / CD = BA/EA 8) By Basic proportionality theorem(EC ||AD) 9) BD /CD = AB/AE 9) BA = AB and EA = AE 10) BD /CD = AB /AC 10) AE = EC and from(7)

Examples

1) In the given figure, AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, find CE.

Given : AB = 10 cm, AC = 6 cm and BC = 12 cm

By exterior angle bisector theorem

BE / CE = AB / AC

(12 + x) / x = 10 / 6

6( 12 + x ) = 10 x [ by cross multiplication]

72 + 6x = 10x
<
72 = 10x – 6x

72 = 4x

x = 72/4

x = 18

CE = 18 cm

PLZ...... GIVE THUMPS UP..

• 16

You copied all this stuff from http://www.ask-math.com... huh? :-P
Anyways, thanks!!

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