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Similar figures. In Euclidean geometry, two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other.More precisely, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection.
The tangential triangle of a reference triangle (other than a right triangle) is the triangle whose sides are on the tangent lines to the reference triangle's circumcircle at its vertices. [ 64 ] As mentioned above, every triangle has a unique circumcircle, a circle passing through all three vertices, whose center is the intersection of the ...
The gnomon of these two similar triangles is the triangle remaining when the smaller of the two similar isosceles triangles is removed from the larger one. The gnomon is itself isosceles if and only if the ratio of the sides to the base of the original isosceles triangle, and the ratio of the base to the sides of the gnomon, is the golden ratio ...
Many objects in the real world, such as coastlines, are statistically self-similar: parts of them show the same statistical properties at many scales. [2] Self-similarity is a typical property of fractals. Scale invariance is an exact form of self-similarity where at any magnification there is a smaller piece of the object that is similar to ...
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 ...
For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes . Generally composed of straight line segments
Among all quadrilaterals, the shape that has the greatest ratio of its perimeter to its diameter (maximum distance between any two points) is an equidiagonal kite with angles 60°, 75°, 150°, 75°. Its four vertices lie at the three corners and one of the side midpoints of the Reuleaux triangle.
Every triangle can be inscribed in an ellipse, called its Steiner circumellipse or simply its Steiner ellipse, whose center is the triangle's centroid. Every triangle has an infinitude of inscribed ellipses. One of them is a circle, and one of them is the Steiner inellipse which is tangent to the triangle at the midpoints of the sides.