Q. 145.0( 1 Vote )

# In a triangle, the perpendicular from the vertex to the base bisects the base. The triangle isA. right-angledB. isoscelesC. scaleneD. obtuse-angled

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

Now AB CE and AE is transversal

BAD = CED (alternate interior s)

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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