Matching the wrong sides in similar triangles
Two triangles are similar, four lengths are given, and the proportion writes itself — with the wrong sides paired.
Why it happens
The figures are drawn rotated or reflected, so 'the left side' of one triangle is not the left side of the other. Position, not correspondence, drives the pairing.
See the trap
△ABC ~ △DEF with AB = 4, BC = 6, DE = 8. Find EF.
Pairing by how the figure looks — AB with EF: 4/8 = EF/6 → EF = 3.
Pair by letter order: AB↔DE and BC↔EF, so 4/8 = 6/EF → EF = 12.
How to actually fix it
- 1Use the similarity statement's letter order, not the picture, to pair sides.
- 2Write each ratio as small△/big△ consistently.
- 3Redraw the second triangle in the same orientation when confused.
Practice this trap · 4 real questions
Each of these is a question from the free bank that turns on the mistake above — the trap is the reason its wrong answer looks right. Easiest first.
FAQ
How do I find corresponding sides fast?
In △ABC ~ △DEF: AB↔DE, BC↔EF, AC↔DF — the letter positions in the statement are the map. Trust it over the drawing.
How do I stop repeating this mistake?
Reading the explanation isn't enough — your brain needs to beat the trap on a fresh question. Practice the skill in the kaoshen.co question bank: miss one and it is logged with the exact error, then brought back to you three days later and again after fourteen.
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