Verifying right triangle using distance
A triangle is right-angled if its side lengths satisfy the Pythagorean relation with the longest side.
Practice This ConceptMain explanation
Teacher explanation
In coordinate geometry, first calculate all three sides using the distance formula. Then identify the longest side and check whether its square equals the sum of the squares of the other two sides. This is the cleanest way to verify a right triangle from coordinates.
Example
For points (0, 0), (3, 0), and (3, 4), the side lengths are 3, 4, and 5, so 3^2 + 4^2 = 5^2.
Simple analogy
Longest side first, then Pythagoras.
Common confusion
Students often choose the wrong side as the hypotenuse or forget to check the longest side first.
Exam tip
Always find the longest side before applying Pythagoras. The largest side must be tested as the hypotenuse candidate.
Answer writing and exam use
1-mark use
Write the exact meaning of verifying right triangle using distance in one clean line.
2-mark use
Define verifying right triangle using distance and add one example or condition.
3-mark use
Explain verifying right triangle using distance, show the method or example, and mention the common mistake.
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