Similar triangles are scaled copies of each other — same shape, different size. Every angle matches its partner, and every pair of corresponding sides is in the same ratio (the scale factor).
Drag the corners
angles sum ≈ 180°
Tests for similarity
- AA — two angles of one match two of the other (so the third does too). The easiest test.
- SSS (ratio) — all three pairs of sides are in the same ratio.
- SAS (ratio) — two pairs of sides in the same ratio with equal included angles.
- Once similar, *all* lengths scale by the same factor — sides, perimeters, heights — and areas scale by the factor squared.
Your turn
Two triangles are similar. The small one has a side of 4 cm matching a 10 cm side of the big one. A different side of the small one is 6 cm — how long is the matching side of the big one?
Similar triangles are how you measure the unreachable — the height of a tree from its shadow, the distance to a ship, the size of the Moon. Set up two triangles with equal angles and let the ratios do the work.