Prove analytically : The line segment joining the midpoints of two sides of a triangle is parallel to the third and half of its length.

Prove by vector method that the line segment joining the mid points of two sides of a triangle is parallel to the third and half of it.

Prove analytically : The perpendicular bisector of the sides of a triangle are concurrent.

Prove that the lines joining the midpoints of consecutive sides of a quadrilateral form a parallelogram using vector method.

Prove by vector method that the lines joining the mid points of consecutive sides of a quadrilateral is a parallelogram.

If M is the midpoint of the side vec(BC) of a triangle ABC, prove that vec(AB)+vec(AC) = 2vec(AM)

Prove by vector method that in a parallelogram, the line joining a vertex to the midpoint of an oppositeside trisects the other diagonal.

What is the area of a triangle formed with two vectors as its two sides ?

Prove that the area of any triangle is equal to four times the area of the triangle formed by joining the mid points of its sides.

The lengths of the largest side of a quadrilateral is three times that of its smallest side. Out of the other two sides length of one is twice that of the smallest and the other is 1 cm. longer than the smallest. If the perimeter of the quadrilateral is at most 36 cm. then find the maximum possible lengths of its sides.