If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.

If the altitude from one vertex of a triangle bisects the opposite side, then the triangle is isosceles. GIVEN : A A B C such that the altitude A D from A on the opposite side B C bisects B C i.e., B D=D Cdot TO PROVE : A B=A C i.e. the triangle A B C is isosceles.

If the bisector of the vertical angle of a triangle bisects the base of the triangle. then the triangle is isosceles. GIVEN : triangle A B C in which A D is the bisector of angle A meeting B C in D such that B D=DC TO PROVE : triangleA B C is an isosceles triangle.

Which of the following statements are true (T) and which are false (F): Side opposite to equal angles of a triangle may be unequal. Angle opposite to equal sides of a triangle are equal. The measure of each angle of an equilateral triangle is 60^0 If the altitude from one vertex of a triangle bisects the opposite side, then the triangle may be isosceles. The bisectors of two equal angles of a triangle are equal. If the bisector of the vertical angle of a triangle bisects the base, then the triangle may be isosceles. The two altitudes corresponding to two equal sides of a triangle need not be equal. If any two sides of a right triangle are respectively equal to two sides of other right triangle, then the two triangles are congruent. 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, prove that the triangle is isosceles.

If the altitudes from two vertices of a triangle to the opposite sides are equal, prove that the triangle is isosceles.

If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.

If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.

If the bisectors of the base angles of a triangle enclose an angle of 135^0, prove that the triangle is a right triangle.

If the bisectors of the base angles of a triangle enclose an angle of 135^0, prove that the triangle is a right triangle.

The external angle bisector of an angle of a triangle divides the opposite side externally in the ratio of the sides containing the angle.