I wrote an earlier blog on this subject but thought it might be useful to break it down into a series of teacher to student questions and instructions to get a more active learning experience in the classroom. This can…

# Geometry

## The angle inscribed in a semi-circle is a right angle.

Take any semi-circle, join two straight lines from each end of the diameter at an apex on the circumference and this angle will always be a right angle. This is one of the more accessible of the circle theorems to…

## Reasoning behind the shortcuts 1: Angles in any triangle sum to 180˚

Angles in any triangle sum to 180˚ I remember being given this piece of information at school and I have always remembered it. I was never told why it was true for all triangles however, I was simply required to…

## Calculating areas of polygons with (x, y) coordinate vertices.

Calculating the area of a triangle is a straight forward task. We simply multiply the base length by its vertical height and then divide it all by 2. All very well if we are given the base and vertical height…

## Teaching trigonometry – calculating unknown angles

The last blog that looked at trigonometry focused on how to calculate an unknown side. This blog post will look at how we can use trigonometry to calculate an unknown angle in a right-triangle. This type of calculation is best…

## The formulae for the area of a triangle. (Part 3 – Scalene.)

In the previous blogs we have seen that the area for any right-triangle and any isosceles triangle (to include the special equilateral triangle) has given up the formula area = bh/2. We should now move on to the next type…

## The formulae for the area of a triangle. (Part 2 – Isosceles.)

In the previous blog we looked at why the formula for the area of a right-triangle is bh/2 where b is the base length and h is the vertical height of the triangle. It is important to note that this…

## The formulae for the area of a triangle. (Part 1 – The right-triangle.)

In the national curriculum for mathematics in England pupils are not required to calculate areas of rectangles, never mind triangles, until year 5 when the statutory requirement states: However go back to the year 1 programme of study it states…

## Teaching trigonometry – calculating unknown sides

In a previous blog we looked at how we might consider introducing trigonometry through the three main trig ratios for sines, cosines and tangents of angles in right-triangles. To recap, we saw that the sine of 30˚ was equal to 1/2…

## Teaching trigonometry – Introducing and explaining trig ratios

Before students start to study trigonometry it should be that they have grasped with confidence Pythagoras’ theorem and the ability to transpose formulae by making any element of a given equation the subject by rearranging. Example: Rearrange 4r -p…