If altitude from one vertex bisects the opposite side, then the triangle is isosceles.

True

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False

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Solution

The correct option is B False
Properties of Isosceles triangle.
If altitude from one vertex bisects the opposite side, then the triangle is not isosceles.
Isosceles triangle: it has two sides equal in length and the angles opposite to these two sides are equal in measure.
Because a altitude drawn from one vertex is perpendicular to the opposite side, hence it does not satisfy the conditions required to be an isosceles triangle.
Hence, the given statement is false.

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Similar questions

Which of the following statements are true (T) and which are false (F):

(i) Sides opposite to equal angles of a triangle may be unequal.

(ii) Angles opposite to equal sides of a triangle are equal.

(iii) The measure of each angle of an equilateral triangle is $60^{\circ}$

(iv) If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

(v) The bisectors of two equal angles of a triangle are equal.

(vi) If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles.

(vii) The two altitudes corresponding to two equal sides of the triangle need not be equal

(viii) If any two sides of a right triangle are respectively equal to two sides of another right triangle, then the two triangles are congruent.

(ix) Two right triangles are congruent if hypotenuse and a side of one triangle are respectively equal to the hypotenuse and a side of the other triangle.

Prove that a ΔABC is an isosceles triangle if the altitude AD from A on BC bisects BC.

Q. If the bisector of an angle of a triangle bisects the opposite side, then the triangle is
(a) scalene
(b) equilateral
(c) isosceles
(d) right-angled

Q. Does the altitude of a triangle drawn from a vertex to the opposite side, bisects the side .

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

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