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2. Congruence (geometry) - Wikipedia

   en.wikipedia.org/wiki/Congruence_(geometry)

   For two polygons to be congruent, they must have an equal number of sides (and hence an equal number—the same number—of vertices). Two polygons with n sides are congruent if and only if they each have numerically identical sequences (even if clockwise for one polygon and counterclockwise for the other) side-angle-side-angle-... for n sides ...

3. Wallace–Bolyai–Gerwien theorem - Wikipedia

   en.wikipedia.org/wiki/Wallace–Bolyai–Gerwien...

   Since both the first polygon and the second polygon are scissors-congruent to the intermediate, they are scissors-congruent to one another. The proof of this theorem is constructive and doesn't require the axiom of choice , even though some other dissection problems (e.g. Tarski's circle-squaring problem ) do need it.

4. Straightedge and compass construction - Wikipedia

   en.wikipedia.org/wiki/Straightedge_and_compass...

   [2]: p. 1 They could also construct half of a given angle, a square whose area is twice that of another square, a square having the same area as a given polygon, and regular polygons of 3, 4, or 5 sides [2]: p. xi (or one with twice the number of sides of a given polygon [2]: pp. 49–50 ).

5. Constructible polygon - Wikipedia

   en.wikipedia.org/wiki/Constructible_polygon

   A regular polygon with n sides can be constructed with ruler, compass, and angle trisector if and only if =, where r, s, k ≥ 0 and where the p i are distinct Pierpont primes greater than 3 (primes of the form +). [8]: Thm. 2 These polygons are exactly the regular polygons that can be constructed with Conic section, and the regular polygons ...

6. Corresponding sides and corresponding angles - Wikipedia

   en.wikipedia.org/wiki/Corresponding_sides_and...

   The orange and green quadrilaterals are congruent; the blue one is not congruent to them. Congruence between the orange and green ones is established in that side BC corresponds to (in this case of congruence, equals in length) JK, CD corresponds to KL, DA corresponds to LI, and AB corresponds to IJ, while angle ∠C corresponds to (equals) angle ∠K, ∠D corresponds to ∠L, ∠A ...

7. Similarity (geometry) - Wikipedia

   en.wikipedia.org/wiki/Similarity_(geometry)

   If two angles of a triangle have measures equal to the measures of two angles of another triangle, then the triangles are similar. Corresponding sides of similar polygons are in proportion, and corresponding angles of similar polygons have the same measure. Two congruent shapes are similar, with a scale factor of 1. However, some school ...

8. Bisection - Wikipedia

   en.wikipedia.org/wiki/Bisection

   Construction by straight edge and compass. In classical geometry, the bisection is a simple compass and straightedge construction, whose possibility depends on the ability to draw arcs of equal radii and different centers:

9. Regular polygon - Wikipedia

   en.wikipedia.org/wiki/Regular_polygon

   Some regular polygons are easy to construct with compass and straightedge; other regular polygons are not constructible at all. The ancient Greek mathematicians knew how to construct a regular polygon with 3, 4, or 5 sides, [11]: p. xi and they knew how to construct a regular polygon with double the number of sides of a given regular polygon.