Verifying isosceles triangle using distance
A triangle is isosceles if two of its sides are equal in length.
Practice This ConceptMain explanation
Teacher explanation
On coordinate planes, side lengths should be checked with the distance formula rather than by eye. A sketch can mislead because the graph may not look perfectly balanced. If two calculated side lengths are equal, the triangle is isosceles.
Example
For A(1, 2), B(5, 2), and C(3, 6), AB = 4 and AC = BC = sqrt(20), so the triangle is isosceles.
Simple analogy
Equal distances, not equal-looking lines.
Common confusion
Students often judge isosceles shape only from the picture and forget to calculate the side lengths.
Exam tip
Always compare the actual distances. Equal-looking sides on a sketch are not enough.
Answer writing and exam use
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Write the exact meaning of verifying isosceles triangle using distance in one clean line.
2-mark use
Define verifying isosceles triangle using distance and add one example or condition.
3-mark use
Explain verifying isosceles triangle using distance, show the method or example, and mention the common mistake.
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