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Any two equilateral triangles are similar. Two triangles, both similar to a third triangle, are similar to each other (transitivity of similarity of triangles). Corresponding altitudes of similar triangles have the same ratio as the corresponding sides. Two right triangles are similar if the hypotenuse and one other side have lengths in the ...
A similarity system of triangles is a specific configuration involving a set of triangles. [1] A set of triangles is considered a configuration when all of the triangles share a minimum of one incidence relation with one of the other triangles present in the set. [1]
The pons asinorum in Oliver Byrne's edition of the Elements [1]. In geometry, the theorem that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum (/ ˈ p ɒ n z ˌ æ s ɪ ˈ n ɔːr ə m / PONZ ass-ih-NOR-əm), Latin for "bridge of asses", or more descriptively as the isosceles triangle theorem.
Figure 1: The point O is an external homothetic center for the two triangles. The size of each figure is proportional to its distance from the homothetic center. In geometry, a homothetic center (also called a center of similarity or a center of similitude) is a point from which at least two geometrically similar figures can be seen as a dilation or contraction of one another.
English: Simplified version of similar triangles proof for Pythagoras' theorem. In triangle ACB, angle ACB is the right angle. CH is a perpendicular on hypotenuse AB of triangle ACB. In triangle AHC and triangle ACB, ∠AHC=∠ACB as each is a right angle. ∠HAC=∠CAB as they are common angles at vertex A.
The smallest 5-Con triangles with integral sides. In geometry, two triangles are said to be 5-Con or almost congruent if they are not congruent triangles but they are similar triangles and share two side lengths (of non-corresponding sides). The 5-Con triangles are important examples for understanding the solution of triangles. Indeed, knowing ...
Similarity (geometry)#Similar triangles To a section : This is a redirect from a topic that does not have its own page to a section of a page on the subject. For redirects to embedded anchors on a page, use {{ R to anchor }} instead .
English: A similarity proof for Pythagoras' theorem based upon areas proportional to sides on the centre triangle. Area of triangle C = sum of areas of A and B. All three right triangles are similar, so all three areas are proportional to the side bordering the centre triangle.