Q. 145.0( 1 Vote )

In a triangle, the perpendicular from the vertex to the base bisects the base. The triangle is
A. right-angled

B. isosceles

C. scalene

D. obtuse-angled

Answer :


In Δ ABC, AD bisects A and meets BC in D such that BD = DC


Extend AD to E and join C to E such that CE is to AB


BAD = CAD


Now AB CE and AE is transversal


BAD = CED (alternate interior s)


But BAD = CED = CAD


In Δ AEC


CEA = CAE


AC = CE………………. 1


In Δ ABD and Δ DCE


BAD = CED (alternate interior s)


ADB = CDE (vertically opposite s)


BD = BC (given)


Δ ABD Δ DCE


AB = EC (CPCT)


AC = EC (from 1)


AB = AC


ABC is an isosceles Δ with AB = AC

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