Given its long history, there are numerous proofs (more than 350) of the Pythagorean theorem, perhaps more than any other theorem of mathematics. The proofs below are by no means exhaustive, and …

The reflexive property of congruence is often used in geometric proofs when certain congruences need to be established. For example, to prove that two triangles are congruent, 3 congruences need to be …

Proof by contradiction (also known as indirect proof or the method of reductio ad absurdum) is a common proof technique that is based on a very simple principle: something that leads to a …

A conjecture is a mathematical statement that has not yet been rigorously proved. Conjectures arise when one notices a pattern that holds true for many cases. However, just because a pattern holds …

Take a guided, problem-solving based approach to learning Geometry. These compilations provide unique perspectives and applications you won't find anywhere else. Geometry and Measurement …

Thus, two triangles with the same sides will be congruent. (Note: If two triangles have three equal angles, they need not be congruent. All that we know is these triangles are similar.) SAS: "Side, …

Finding the Incenter All triangles have an incenter, and it always lies inside the triangle. One way to find the incenter makes use of the property that the incenter is the intersection of the three angle …

Hyperbolic geometry is a type of non-Euclidean geometry that arose historically when mathematicians tried to simplify the axioms of Euclidean geometry, and instead discovered unexpectedly that …

The Euler line of a triangle is a line going through several important triangle centers, including the orthocenter, circumcenter, centroid, and center of the nine point circle. The fact that such a line …

In linear algebra, the rank of a matrix is the dimension of its row space or column space. It is an important fact that the row space and column space of a matrix have equal dimensions. Intuitively, …