Prove that the Iine joining the midpoints of the two sides of a triangle is parallel to the third side and half of its length.

Show that the line segment joining the midpoints of two 'sides of a triangle is parallel to. the third side and is half its length using vectors.

Prove that the quadrilatral formed by joining the mid points of the sides of a quadrilateral is a parallelogram.

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.

Prove that the two circles drawn on the two equal sides of an isosceles triangle as diameters pass through the mid point of the third side.

In the picture, the perpendicular is drawn from the midpoint of the hypotenuse of a right triangle. to the base. Calculate the length of the third side of the large right triangle and the lengths of all three sides of the small right triangle.

Prove that the lengths of the perpendiculars from any point on the bisector of an angle to the sides are equal.

In the picture below, two lines are drawn from the top vertex of a triangle to the bottom side: Prove that the ratio in which these lines divide the length of the bottom side is equal to the ratio of the area of the three smaller triangles in the picture.

Prove the radius of the Incircle of an equilateral triangle is half the radius of its circumclrcle.