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Question

Show that the angle bisector of vertical angle of isosceles triangle, bisects the base i.e. it is an median.

(i) (ii)

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Solution



Given : AD is the angle bisector BAD = DACAB = AC (ABC is isosceles)In ABD and ACD,AB = AC BAD = CAD,AD = AD (common)Thus, ABD ACD ( by SAS congruency test)BD = CD ( by c.s.c.t)Therefore, the angle bisector of the vertical angle of an isosceles triangle bisects the base.

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