Prove by vector method that the diagonals of a rhombus bisect each other at right angles.

The diagonals of rhombus bisect each other at . . . . . . .

Using vectors prove that the diagonals of a parallelogram bisect each other.

Using vector method, prove that if the diagonals of a parallelogram are equal, then it is a rectangle.

Prove that the area of a rhombus is equal to half of the product of the diagonals.

Show that the diagonals of a square are equal and right bisectors of each other.

Prove by vector method that the perpendiculars (altitudes) from the vertices to the sides of a triangle are concurrent.

Prove by vector method that the parallelograms on the same base and between the same parallels are equal in area.

Prove by vector method that an angle in a semi-circle is a right angle.