Corresponding sides in the context of Similarity (geometry)

⭐ Core Definition: Corresponding sides

In geometry, the tests for congruence and similarity involve comparing corresponding sides and corresponding angles of polygons. In these tests, each side and each angle in one polygon is paired with a side or angle in the second polygon, taking care to preserve the order of adjacency.

For example, if one polygon has sequential sides $a$ , $b$ , $c$ , $d$ , and $e$ and the other has sequential sides $v$ , $w$ , $x$ , $y$ , and $z$ , and if $b$ and $w$ are corresponding sides, then side $a$ (adjacent to $b$ ) must correspond to either $v$ or $x$ (both adjacent to $w$ ). If $a$ and $v$ correspond to each other, then $c$ corresponds to $x$ , $d$ corresponds to $y$ , and $e$ corresponds to $z$ ; hence the $i$ th element of the sequence $abcde$ corresponds to the $i$ th element of the sequence $vwxyz$ for $i = 1, 2, 3, 4, 5.$ On the other hand, if in addition to $b$ corresponding to $w$ we have $c$ corresponding to $v$ , then the $i$ th element of $abcde$ corresponds to the $i$ th element of the reverse sequence $xwvzy$ .

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Corresponding sides in the context of Prism (geometry)

In geometry, a prism is a polyhedron comprising an $n$ -sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and $n$ other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Prisms are named after their bases, e.g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids.

Like many basic geometric terms, the word prism (from Greek πρίσμα (prisma) 'something sawed') was first used in Euclid's Elements. Euclid defined the term in Book XI as "a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms". However, this definition has been criticized for not being specific enough in regard to the nature of the bases (a cause of some confusion amongst generations of later geometry writers).

View the full Wikipedia page for Prism (geometry)

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Corresponding sides in the context of Similarity (geometry)

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⭐ Core Definition: Corresponding sides

Corresponding sides in the context of Prism (geometry)