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2. 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.

3. 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 ...

4. Congruum - Wikipedia

   en.wikipedia.org/wiki/Congruum

   A congruent number is defined as the area of a right triangle with rational sides. Because every congruum can be obtained (using the parameterized solution) as the area of a Pythagorean triangle, it follows that every congruum is congruent. Conversely, every congruent number is a congruum multiplied by the square of a rational number. [7]

5. Euclidean geometry - Wikipedia

   en.wikipedia.org/wiki/Euclidean_geometry

   Thus, for example, a 2x6 rectangle and a 3x4 rectangle are equal but not congruent, and the letter R is congruent to its mirror image. Figures that would be congruent except for their differing sizes are referred to as similar. Corresponding angles in a pair of similar shapes are equal and corresponding sides are in proportion to each other.

6. Solution of triangles - Wikipedia

   en.wikipedia.org/wiki/Solution_of_triangles

   Assume that two sides b, c and the angle β are known. The equation for the angle γ can be implied from the law of sines: [5] ⁡ = ⁡. We denote further D = ⁠ c / b ⁠ sin β (the equation's right side). There are four possible cases:

7. Similarity (geometry) - Wikipedia

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

   The ratio between the areas of similar figures is equal to the square of the ratio of corresponding lengths of those figures (for example, when the side of a square or the radius of a circle is multiplied by three, its area is multiplied by nine — i.e. by three squared). The altitudes of similar triangles are in the same ratio as ...

8. Congruence (geometry) - Wikipedia

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

   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. [ 1 ] More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry , i.e., a combination of rigid motions , namely a ...

9. Bracket (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Bracket_(mathematics)

   In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets , are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take ...