QCE Together Year 12 Specialist Maths: Geometric Results of Vectors

Specialist Maths

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Geometric Results of Vectors

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.

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