WJEC MATHEMATICS
INTERMEDIATE
ANGLES AND GEOMETRY
PYTHAGORAS' THEOREM
1
Contents
Finding the hypotenuse
Finding a shorter side
Checking something is a right angled triangle
Worded Question
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
TES - pfellowes
Pythagoras Worksheet
https://www.tes.com/teaching-resource/pythagoras-worksheet6325033
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Pythagoras' Theorem
Pythagoras' Theorem is used when finding lengths in right angled
triangles. The theorem is a link between the hypotenuse and the
other two sides.
The hypotenuse is
always opposite the
right angle
(represented by the
square)
The equation needed to find the length of the hypotenuse is;
Example
Find the length of the hypotenuse in the following triangle
Using Pythagoras' Theorem
Square root both sides
to get P on its own.
So the longer side is 20cm
3
Finding the length of a shorter side
In some cases, you will need to find the length of one of the smaller
sides. For this, you will need to rearrange the formula to find the
unknown value. (See the Rearranging' booklet for more help on this)
This is the
hypotenuse.
So, Pythagoras' theorem tells us
Now, we need to subtract
in the previous example
from both sides and then solve as seen
Remember to
give your
answer to a
sensible
number of
decimal places
Another way of thinking of this is
"to find a shorter side, square the hypotenuse and subtract the
other side squared".
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Exercise G21
1. Find the value of the sides of these triangles labelled with a letter
2. Find the value of the sides of these triangles labelled with a letter
3. Find the perimeter of the following triangles
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Checking a triangle is Right Angled
We can check if a triangle is right angled by using Pythagoras'
Theorem. If
then the triangle is right angled.
Example 1
Verify that a triangle with lengths 5cm, 4cm, and 3cm is a right
angled triangle
The longest side is the hypotenuse in a right angled triangle
So,
So this is a right angled triangle
Example 2
Verify that a triangle with lengths 5cm, 7cm, and 9cm is a right
angled triangle
So this is not a right angled triangle
Exercise G22
1. Verify that a triangle with lengths 10cm, 8cm, 6cm is a right angled
triangle
2. Verify that a triangle with lengths 15cm, 12cm, 13cm is a right
angled triangle
3. Verify that a triangle with lengths 16cm, 11cm, 12cm is a right
angled triangle
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Worded/Picture Questions
Some questions describe a scenario instead of giving you the
question as a diagram. To make these questions easier, turn the
words into a diagram.
Example
Jack places a 9m ladder against a wall. If he is standing 3m away
from the wall, how high up the wall will the ladder reach?
Turning this into a diagram
Wall
Ladder
9m
3m
Floor
So, you can see the right angled triangle here
Remember to
give your
answer to a
sensible
number of
decimal places
So the ladder will reach 8.49m up the wall.
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Exam Questions G34
1.
2.
3.
8
4.
5.
9