This is part of the QCE Specialist Maths course under Unit 3: Mathematical induction, and further vectors, matrices and complex numbers, specifically topic 2: vectors and matrices and reviewing the concepts of vectors from Unit 1. 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.
