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

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

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Solution

Given: The altitude from one vertex of a triangle bisects the opposite side

In $△ A B D a n d △ A C D$

AD = AD

$∠ A D B = ∠ A D C$

BD = DC

$∴ △ A D B ≅ △ A D C$ (By SAS Congruence criterion)

Thus, AB = AC (C.P.C.T)

Therefore, the triangle is an isosceles.

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

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.

If the altitudes from two vertices of a triangle to the opposite sides are equal then the triangle is

(a) equilateral (b) isosceles

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

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°.

(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 a triangle need not be equal.

(viii) If any two sides of a right triangle are respectively equal to two sides of other 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 equal to the hypotenuse and a side of the other triangle.

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

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Which of the following statements are true(T) which are false (F). If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles.

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

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