If a line through one vertex of a triangle divides the opposite sides in the Ratio of other two sides; then the line bisects the angle at the vertex.

Read the statemenst carefully and state 'T' for true and 'F' for false . 1. If a line divides any two sides of a triangle in the same ratio , then the line is parallel to the third side of the triangle . 2 . The internal bisector of an angle of a triangle divides the opposite side inernally in the ratio of the sides containing the angle . 3 . If a line through one vertex of a triangle divides the opposite in the ratio of other two sides , then the line bisects the angle at the vertex . 4.Any line parallel to the parallel sides dividesproportionally . 5. Two times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle .

If the altitude from one vertex of a triangle bisects the opposite side; then the triangle is isosceless.

The internal angle bisector of an angle of a triangle divide the opposite side internally in the ratio of the sides containgthe angle

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

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 square of one side of a triangle is equal to the sum of the squares of the other two sides then the triangle is a right triangle with the angle opposite the first sides as right angle.

Through each vertex of a triangle, a line parallel to the opposite side is drawn. The ratio of the perimeter of the new triangle, thus formed, with that of the original triangle is

A vertex of an equilateral triangle is (2,3) and the opposite side is x+y=2. Find the equations of other sides.

A vertex of an equateral triangle is (2,3) and the opposite side is x + y =2. The equaiton of other sides are