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2. Dividing a square into similar rectangles - Wikipedia

   en.wikipedia.org/wiki/Dividing_a_square_into...

   However, there are three distinct ways of partitioning a square into three similar rectangles: [1] [2] The trivial solution given by three congruent rectangles with aspect ratio 3:1. The solution in which two of the three rectangles are congruent and the third one has twice the side length of the other two, where the rectangles have aspect ...

3. 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 ...

4. Hilbert's third problem - Wikipedia

   en.wikipedia.org/wiki/Hilbert's_third_problem

   Dehn's proof is an instance in which abstract algebra is used to prove an impossibility result in geometry.Other examples are doubling the cube and trisecting the angle.. Two polyhedra are called scissors-congruent if the first can be cut into finitely many polyhedral pieces that can be reassembled to yield the second.

5. Congruence (geometry) - Wikipedia

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

   The two triangles on the left are congruent. The third is similar to them. The last triangle is neither congruent nor similar to any of the others. 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.

6. AA postulate - Wikipedia

   en.wikipedia.org/wiki/AA_postulate

   In Euclidean geometry, the AA postulate states that two triangles are similar if they have two corresponding angles congruent. The AA postulate follows from the fact that the sum of the interior angles of a triangle is always equal to 180°. By knowing two angles, such as 32° and 64° degrees, we know that the next angle is 84°, because 180 ...

7. 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 ...

8. Ed Sheeran responds to criticism after crashing Ruben Amorim ...

   www.aol.com/news/ed-sheeran-responds-criticism...

   Ed Sheeran has apologised to Ruben Amorim after gatecrashing a Sky Sports interview with the new Manchester United manager.. Amorim was speaking to presenter Kelly Cates as well as pundits Roy ...

9. Elementary mathematics - Wikipedia

   en.wikipedia.org/wiki/Elementary_mathematics

   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. [8] 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 translation , a ...