Enter a matching side pair to scale another triangle, or compare two complete side sets with an SSS similarity check and transparent proportional ratios.
Verify scale factor, corresponding sides, perimeter and area ratios, triangle validity and a side-by-side proportional diagram.
Keep linear inputs in a consistent unit, verify that side lengths or coordinate points can form the stated shape, and treat sketches as explanatory unless explicitly marked to scale. Coordinate formulas can become unstable for nearly degenerate shapes, so invalid or nearly collinear inputs are rejected rather than silently returning misleading values.
Similarity depends on side correspondence, not simply sorting three lengths from smallest to largest in every real diagram. Identify which vertices or sides correspond using the geometry, then compare ratios. A wrong correspondence can produce a neat scale factor that belongs to a different pairing and therefore solves the wrong triangle.
Three proportional side pairs establish SSS similarity, while AA and SAS can establish similarity from different information. If only angles or one included angle with side ratios are known, use a solver designed for that proof rather than inventing missing lengths. The calculator’s mode should match the evidence actually supplied by the problem.
If one triangle is k times as large in corresponding side lengths, its perimeter scales by k but its area scales by k². This distinction matters when using a similar-triangle result to estimate material, map area, shadow geometry, or a scaled drawing. Do not apply the linear scale factor directly to an area quantity.
After a missing side is solved, divide it by its corresponding side in the other triangle and compare that ratio with the other matched pairs. Consistent ratios provide an independent arithmetic check. Large discrepancies can indicate a transcription or correspondence error even when the direct multiplication step itself was calculated correctly.
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