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Interior 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!!! Interior Angle Bisector Theorem : The angle bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.Given : A ΔABC in which AD is the internal bisector of ∠A and meets BC in D. Prove that : BD / DC = AB / AC Construction : Draw CE  DA to meet BA produced in E.
_________________________________________________________________ Examples 1) In the given figure, AD is the bisector of ∠A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, find AC. Solution : In Δ ABC, AD is the bisector of ∠A. ∴ BD / DC = AB / AC ( Angle bisector theorem) ⇒ 4 / 3 = 6 / AC ⇒ 4 AC = 18 ⇒ AC = 18 / 4 = 4.5 cm.  2) AD is a median of ΔABC. The bisector of ∠ADB and ∠ADC meet AB and AC in E and F respectively. Given : In ΔABC, AD is the median and DE and DF are angle bisectors of ∠ADB and ∠ADC respectively. Prove that : EF  BC
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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