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Exterior Angle Bisector TheoremCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! 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.
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 2) The bisector of interior ∠A of ΔABC meets BC in D, and the bisector of exterior ∠A meets BC produced in E. Prove that BD / BE = CD / CE. Given : In ΔABC, AD and AE are respectively the bisectors of the interior and exterior angles at A. Prove that : BD/BE = CD/CE
Similarity in Triangles • Similarity in Geometry • Properties of similar triangles • Basic Proportionality Theorem(Thales theorem) • Converse of Basic Proportionality Theorem • Interior Angle Bisector Theorem • Exterior Angle Bisector Theorem • Proofs on Basic Proportionality • Criteria of Similarity of Triangles • Geometric Mean of Similar Triangles • Areas of Two Similar Triangles Covid19 has affected physical interactions between people. Don't let it affect your learning.
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