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2. Thales's theorem - Wikipedia

   en.wikipedia.org/wiki/Thales's_theorem

   Thales's theorem. Angle formed by a point on a circle and the 2 ends of a diameter is a right angle. Thales’ theorem: if AC is a diameter and B is a point on the diameter's circle, the angle ∠ ABC is a right angle. In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the ...

3. Miquel's theorem - Wikipedia

   en.wikipedia.org/wiki/Miquel's_theorem

   Miquel's theorem. Miquel's theorem is a result in geometry, named after Auguste Miquel, [1] concerning the intersection of three circles, each drawn through one vertex of a triangle and two points on its adjacent sides. It is one of several results concerning circles in Euclidean geometry due to Miquel, whose work was published in Liouville's ...

4. Inscribed angle - Wikipedia

   en.wikipedia.org/wiki/Inscribed_angle

   Supplementary inscribed angle θ on minor arc. In geometry, an inscribed angle is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle subtended at a point on the circle by two given points on the circle. Equivalently, an inscribed angle is defined by two chords of the circle ...

5. Similarity (geometry) - Wikipedia

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

   The concept of similarity extends to polygons with more than three sides. Given any two similar polygons, corresponding sides taken in the same sequence (even if clockwise for one polygon and counterclockwise for the other) are proportional and corresponding angles taken in the same sequence are equal in measure.

6. Congruence (geometry) - Wikipedia

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

   Congruence (geometry) Relationship between two figures of the same shape and size, or mirroring each other. 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 ...

7. Menelaus's theorem - Wikipedia

   en.wikipedia.org/wiki/Menelaus's_theorem

   Menelaus's theorem. In Euclidean geometry, Menelaus's theorem, named for Menelaus of Alexandria, is a proposition about triangles in plane geometry. Suppose we have a triangle ABC, and a transversal line that crosses BC, AC, AB at points D, E, F respectively, with D, E, F distinct from A, B, C. A weak version of the theorem states that.