Test for a right angle
Objective. Use the converse of Pythagoras to classify triangles.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
- 5. Continue
Learn: the key idea
The converse of Pythagoras' theorem lets you test whether a triangle has a right angle just from its three side lengths. Square all three sides, then check whether the sum of the two smaller squares equals the largest square; if it does, the triangle is right-angled, and if not, it is not. Example: for sides 5, 12 and 13, check 5² + 12² = 25 + 144 = 169, which equals 13² = 169, so this is a right-angled triangle. If the sum of the smaller squares is less than the largest square the triangle is obtuse, and if greater it is acute.
Worked example
A triangle has sides of length 7 cm, 24 cm and 25 cm. Use the converse of Pythagoras to test whether it contains a right angle.
- 1Identify the largest side as 25 cm and square all three sides: 7² = 49, 24² = 576, 25² = 625.
- 2Add the two smaller squares: 49 + 576 = 625.
- 3Compare this sum with the largest square: 625 equals 625.
- 4Since the sums are equal, the triangle does contain a right angle.
Answer: Yes, it is right-angled
Concept mastery
Based on your past attempts at this lesson — the question types to practise again come first.
Complete a practice set to see your concept breakdown here.
Practice
Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.
Start practisingCommon mistake. Pupils sometimes assume any triangle with a long side must be right-angled without checking the squares; always test numerically whether the two smaller squares sum to the largest square before concluding.
Your progress
Tick each step as you finish it. Your exact reading position is saved automatically, so Continue drops you back on the same line.
0 of 5 steps complete
Your place saves automatically as you read.