QCE Together Year 12 Specialist Maths: Geometric Results of Vectors

#### Specialist Maths

Back to other subjects

# 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.

### 45,861 students have a head start...

Get exclusive QCE content & advice from our team of experts delivered weekly to your inbox!

## Here’s how we help...

### Holistic K-12 Tutoring

Attend our master-class workshops on how to ace your essays, assessments and exams!

### Comprehensive Workshops

Attend our master-class workshops on how to ace your essays, assessments and exams!

### Study, Uni, Career Mentoring

Attend our master-class workshops on how to ace your essays, assessments and exams!

### Senior School Workshops

Attend our master-class workshops on how to ace your essays, assessments and exams!

## 45,861 students have a head start...

Get exclusive study content & advice from our team of experts delivered weekly to your inbox!