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

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.

In the figure small triangles are drawn joining the mid points of large triangle. Find the length of sides of large triangle.

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

Without drawing coordinate axes mention the positions of 'A(2,1), B(6,1), C(6,5)' as left-right, above-below. Draw coordinate axes, mark the points and complete triangle 'ABC' Which side of the triangle is parallel to 'x' axis . Which side is parallel to 'y' axis Write the coordinates of the midpoint of AB. Write the coordinates of the midpoint of BC. Write the coordinates of the midpoint of AC.