Similarity (geometry)

Similarity is a relation between figures with equal corresponding angles and proportional corresponding lengths. It preserves shape while allowing size to change.

Scale factor: A multiplier that converts one quantity or length into another at a consistent ratio. Corresponding lengths in similar figures differ by this constant multiplier.
AA similarity criterion: A triangle similarity test stating that two equal pairs of corresponding angles guarantee similarity. It establishes triangle similarity without comparing every side.
Thales' theorem: A theorem stating that a line parallel to one side of a triangle cuts the other two sides proportionally. Parallel lines create smaller triangles similar to the original, enabling length calculations.
Affine transformation: A transformation that preserves points, lines, and parallelism but can change angles and length ratios. Unlike similarity transformations, general affine transformations need not preserve shape.
Corresponding angles: Angles occupying matching positions in two geometric figures or constructions. Similarity requires each pair of matching angles to have equal measures.
SSS similarity criterion: A triangle similarity test requiring all three pairs of corresponding sides to have the same ratio. It verifies similarity directly from the three side lengths.
Indirect measurement: A method for finding an inaccessible length or distance by relating it to measurable quantities. Similar triangles can determine heights or distances from accessible measurements.
Isometry: A transformation that preserves distances between all pairs of points. An isometry preserves size, whereas similarity permits uniform scaling.
Proportionality: A relation in which quantities vary by a constant ratio. The side lengths of similar figures satisfy this relation.
SAS similarity criterion: A triangle similarity test using two proportional side pairs and their equal included angle. It combines a length ratio with an angle condition to establish similarity.

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