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

If the median to the base of a triangle is perpendicular to the base then triangle is isosceles.

If the median to the base of a triangle is perpendicular to the base, then 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.

Show that the bisector of vertical angle of an isosceles triangle bisects the base at right angles.

In a triangle A B C , if cos A=(sinB)/(2sinC) , show that the triangle is isosceles.

If A, B, C are the angles of a triangle ABC and if cosA=(sinB)/(2sinC) , show that the triangle is isosceles.