1. Right Angled Triangles
Working with Pythagorean Theorem
Stonemasonry Department 2011

2. Types of Triangles
Isosceles Right Angled
An isosceles triangle has The right angled
two sides of the same triangle consists of one
length and two angles angle of 90° and a side
of the same measure. opposite the right
All angles add to 180° angle known as the
hypotenuse.
Scalene Equilateral
A scalene triangles has An equilateral triangle
three sides of different has three sides of the
lengths and three same length and three
angles of different sizes. identical angles (60°).

3. Right Angled Triangles
The angles are The long diagonal
marked with arcs. If side of a right angled
two angles have the triangle is known as
same number of arcs the hypotenuse.
it means they are
both the same.
All right angled
triangles have an The marks on each side of the
angle which measure triangle indicate that each side is
90°. of different lengths. If two sides
had the same markings it would
mean they share the same length.

4. The Three, Four, Five Rule
a = 5m
b = 3m
c = 4m
The 3,4,5 rule states that if the sides of a right
25m²
angled triangle are 3m and 4m then the
hypotenuse would measure 5m. 9m²
This comes from a theory called pythagoras
theorem which states that:
a² = b² + c² 16m²
Where a, b and c are the names given to the
sides of the right angled triangle

5. Pythagorean Theory
However, not all triangles have sides which
measure 3m, 4m and 5m so how do we check if
they are right angled triangles?
10 x 10 =
100m²
We can still use pythagorean theory which
states that:
36m²
6x6=
a² = b² + c²
Lets look at the triangle below:
64m²
8x8=
b = 6m
a = 10m
36m² + 64m² = 100m²
This means that the triangle is a right angled
triangle.
c = 8m

6. Pythagorean Theory
The theory works with all right angled triangles
a² = b² + c² 225m²
Lets look at the triangle below:
81m²
a = 15m 144m²
b = 9m
81m² + 144m² = 225m²
c = 12m
This means that the triangle is a right angled
triangle.

7. Pythagorean Theory
a² = b² + c²
Lets look at the triangle below: 81m²
64m²
a = 9m 25m²
b = 8m
64m² + 25m² = 89m²
c = 5m
This means that the triangle is a NOT a right
angled triangle.

8. Determining Right Angles
Determine whether the triangles shown below are right angled.
a² = b² + c²
a = 25m a = 0.5m
b = 15m b = 0.3m
c = 20m c = 0.4m
a = 89m a = 9m
b = 5m b = 8m
c = 8m c = 5m

9. Finding the Hypotenuse
We can also use the theory to calculate the
length of the hypotenuse provided we know the
triangle is a right angled triangle.
?
a² = b² + c²
Lets look at the triangle below: 16m²
64m²
a = ?m
b = 4m
16m² + 64m² = 80m²
We then find the square root (√)of 82 to
c = 8m determine the length of the hypotenuse:
√80 = 8.94m

10. Finding the Hypotenuse
Determine the length of the hypotenuse for each of the triangles shown below using
pythagoras theory.
a² = b² + c²
a = ?m a = ?m
b = 6m b = 0.4m
a=9.2m a=0.8m
c = 7m c = 0.7m
a = ?m a = ?m
b = 2m b = 8.3m
a=3.6m a=12.8m
c = 3m c = 9.7m

11. Finding the Length of One Side
We can also use the theory to calculate the
length of one side provided we know the
triangle is a right angled triangle.
100m²
a² = b² + c²
Lets look at the triangle below: ?
64m²
a = 10m
b = ?m
? + 64m² = 100m²
So we subtract 64 from 100 to get 36 and
c = 8m then find the square root (√)of 36 to
determine the length of the side:
√36 = 6m

12. Finding the Length of One Side
Determine the length of the missing side for each of the triangles shown below using
pythagoras theory.
a² = b² + c²
a = 18m a = 8.2m
b = 11.3m b = 3.2m
c=14m c=7.6m
c = ?m c = ?m
a = 3m a = 12.5m
b = 1m b = ?m
c=2.8m b=7.9m
c = ?m c = 9.7m

13. Image References
The image on the title slide of this presentation was
sourced from Wikipedia at:
http://en.wikipedia.org/wiki/File:Kapitolinischer_Pythagora
s_adjusted.jpg
This image was made available under creative commons

14. Developed by The Stonemasonry Department
City of Glasgow College
2011