D is a point on side BC of triangle ABC such that BD/CD =AB/AC prove that AD bisects - Maths - Triangles

Question

D is a point on side BC of triangle ABC such that BD/CD =AB/AC
prove that AD bisects angle BAC

Shruti Tyagi · Accepted Answer

Dear student,

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In ∆ABD and ∆ACDAD=AD⇒∠B=∠C                --[equal sides have equal angles opp
 to them]ABAC=BDCD                    --[given]∴∆ABD~∆ACD          [If two sides of one triangle are proportional to two sides of another triangle, and included angle between then then the triangles must be similar]
⇒∠BAD=∠CADHence AD bisects ∠BAC
Regards

D is a point on side BC of triangle ABC such that BD/CD =AB/AC . prove that AD bisects angle BAC