This topic is part of the HSC Mathematics Extension 1 syllabus under the topic Vectors.

In this post, we will explore the geometric results of vectors. In particular, we will cover:

- The diagonals of a parallelogram meet at right angles if and only if it is a rhombus
- The midpoints of the sides of a quadrilateral join to form a parallelogram
- The sum of the squares of the lengths of the diagonals of a parallelogram is equal to the sum of the squares of the lengths of the sides

### Diagonal of a rhombus

The diagonals of a parallelogram meet at right angles if and only if it is a rhombus.

### The midpoint of a parallelogram

The midpoints of the sides of a quadrilateral join to form a parallelogram.

Finally, the sum of the squares of the lengths of the diagonals of a parallelogram is equal to the sum of the squares of the lengths of the sides. This can be derived using the two theorems found above.