Finding Missing Sides in Similar Triangles

Pre-Algebra · Axiom Academy

EXAMPLE Finding Missing Sides in Similar Triangles Use a proportion of corresponding sides to find an unknown length when two triangles are similar. Triangles and are similar. In the sides are , , and . In the corresponding sides are , , and EF = x . Find the missing side x . Two similar triangles: corresponding sides are in the same position. Nice work! You found a missing side in a pair of similar triangles by building and solving a proportion. Proportional sides: In similar triangles, corresponding sides share one common ratio (here every pair equals the scale factor 1.5 ). Match corresponding sides: Line up sides that sit in the same position before writing the ratio. Build the proportion: Set two ratios of corresponding sides equal: . Cross-multiply and solve: 6x = 90 , so x = 15 cm. Verify: — all scale factors agree, so the answer checks out. This method works for any pair of similar triangles: pick two corresponding sides you know and one with an unknown, then let the shared ratio do the work.

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