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 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.

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.

Altitudes the perpendiculars drawn from the vertices of a triangle to the opposite side are known as the altitudes of the triangle.

BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

The bisectors of the angles B and C of a triangle A B C , meet the opposite sides in D and E respectively. If DE||BC , prove that the triangle is isosceles.

Let the lengths of the altitudes drawn from the vertices of Delta ABC to the opposite sides are 2, 2 and 3. If the area of Delta ABC " is " Delta , then find the area of triangle

Prove that the perpendicular let fall from the vertices of a triangle to the opposite sides are concurrent.

One angle of a triangle is equal to one angle of another triangle and the bisectors of these two equal angles divide the opposite sides in the same ratio, prove that the triangles are similar.

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