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State true or false.

In an isosceles triangle, the altitude from the vertex bisects the base. Justify.

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True

False

answer is A.

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Detailed Solution

Suppose there is a isosceles triangle ABC in which,
AB=BC
Question Image

Drop a perpendicular from A to O.
Here, in triangle

ABO and CBO,

we have,

AB = BC

(isosceles triangle equal sides)

∠ BOC = ∠ BOA = 90^{o}

(right angle)

BO = BO

(common side)
So, from side-angle-side criteria of congruency,

△ AOB ≅ △ COB

So, from corresponding parts of the congruence triangle,

AO = CO

Thus, we can say that altitude from the vertex AO bisect the base BC in isosceles triangle.
So, the given statement is true.
Option 1 is correct.

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