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2. Parallelogram - Wikipedia

   en.wikipedia.org/wiki/Parallelogram

   In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. The congruence of opposite sides and opposite angles is a direct consequence of the ...

3. Polarization identity - Wikipedia

   en.wikipedia.org/wiki/Polarization_identity

   Polarization identity. In linear algebra, a branch of mathematics, the polarization identity is any one of a family of formulas that express the inner product of two vectors in terms of the norm of a normed vector space. If a norm arises from an inner product then the polarization identity can be used to express this inner product entirely in ...

4. Varignon's theorem - Wikipedia

   en.wikipedia.org/wiki/Varignon's_theorem

   The Varignon parallelogram is a rectangle if and only if the diagonals of the quadrilateral are perpendicular, that is, if the quadrilateral is an orthodiagonal quadrilateral. [6]: p. 14 [7]: p. 169 For a self-crossing quadrilateral, the Varignon parallelogram can degenerate to four collinear points, forming a line segment traversed twice.

5. Pythagorean theorem - Wikipedia

   en.wikipedia.org/wiki/Pythagorean_theorem

   In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

6. Congruence (geometry) - Wikipedia

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

   Congruence permits alteration of some properties, such as location and orientation, but leaves others unchanged, like distances and angles. The unchanged properties are called invariants. In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

7. Law of cosines - Wikipedia

   en.wikipedia.org/wiki/Law_of_cosines

   Fig. 1 – A triangle. The angles α (or A), β (or B), and γ (or C) are respectively opposite the sides a, b, and c. In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) relates the lengths of the sides of a triangle to the cosine of one of its angles. For a triangle with sides and opposite respective angles ...

8. Conjugate diameters - Wikipedia

   en.wikipedia.org/wiki/Conjugate_diameters

   Two conjugate diameters of an ellipse. Each edge of the bounding parallelogram is parallel to one of the diameters. For an ellipse, two diameters are conjugate if and only if the tangent line to the ellipse at an endpoint of one diameter is parallel to the other diameter. Each pair of conjugate diameters of an ellipse has a corresponding ...

9. Hilbert's axioms - Wikipedia

   en.wikipedia.org/wiki/Hilbert's_axioms

   The axioms. [] Hilbert's axiom system is constructed with six primitive notions: three primitive terms: [ 5 ] point; line; plane; and three primitive relations: [ 6 ] Betweenness, a ternary relation linking points; Lies on (Containment), three binary relations, one linking points and straight lines, one linking points and planes, and one ...