Back to Edexcel Pythagoras’ Theorem (H) Home
4.9 C) Proving a Triangle is a Right-Angled Triangle
4.9 C) Proving a Triangle is a Right-Angled Triangle
Sometimes in an exam you may be given a potential right-angled triangle and asked to prove whether it is or is not a right-angled triangle. We are able to see whether a triangle is or is not a right-angled triangle by using Pythagoras’ theorem and subbing in the values for the potential right-angled triangle. If the values work in the Pythagoras’ theorem equation, the triangle is a right-angled triangle. If the values do not work in the Pythagoras’ theorem equation, the triangle is not a right-angled triangle. Let’s have an example.
Example 1
Is the triangle below a right-angled triangle?
Is the triangle below a right-angled triangle?
We are going to be using the formula below to see if this triangle is a right-angled triangle.
c in the formula above is the hypotenuse of a right-angled triangle. The hypotenuse of a right-angled triangle is the longest side, which means that the hypotenuse of this triangle is the side that is 15 (c = 15). The other two sides will be a and b; it does not matter which side is a and which side is b. I am going to let a be 12 and b be 9.
The next step is to sub the values for a, b and c into the formula.
This equation holds, which means that the triangle is a right-angled triangle.
Example 2
Is the triangle below a right-angled triangle?
Is the triangle below a right-angled triangle?
We are going to be using the formula below to see if this triangle is a right-angled triangle.
c in the formula above is the hypotenuse of a right-angled triangle. The hypotenuse of a right-angled triangle is the longest side, which means that the hypotenuse of this triangle is the side that is 11 (c = 11). The other two sides will be a and b; it does not matter which side is a and which side is b. I am going to let a be 6 and b be 9.
The next step is to sub the values for a, b and c into the formula.
This equation does not hold as the left side of the equation does not equal the right side of the equation. This means that the triangle above is not a right angled triangle.