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Construct a second triangle with sides of length a and b containing a right angle. By the Pythagorean theorem, it follows that the hypotenuse of this triangle has length c = √ a 2 + b 2, the same as the hypotenuse of the first triangle. Since both triangles' sides are the same lengths a, b and c, the triangles are congruent and
If two triangles satisfy the SSA condition and the length of the side opposite the angle is greater than or equal to the length of the adjacent side (SSA, or long side-short side-angle), then the two triangles are congruent. The opposite side is sometimes longer when the corresponding angles are acute, but it is always longer when the ...
When obtuse triangles are glued in this way, the resulting surface can be folded to form a disphenoid (by Alexandrov's uniqueness theorem) but one with acute triangle faces and with edges that in general do not lie along the edges of the given obtuse triangles. Two more types of tetrahedron generalize the disphenoid and have similar names. The ...
Two sides and an angle not included between them (SSA), if the side length adjacent to the angle is shorter than the other side length. A side and the two angles adjacent to it (ASA) A side, the angle opposite to it and an angle adjacent to it (AAS). For all cases in the plane, at least one of the side lengths must be specified.
The trapezohedra are another family of polyhedra that have congruent kite-shaped faces. In these polyhedra, the edges of one of the two side lengths of the kite meet at two "pole" vertices, while the edges of the other length form an equatorial zigzag path around the polyhedron. They are the dual polyhedra of the uniform antiprisms. [36]
These include the Calabi triangle (a triangle with three congruent inscribed squares), [10] the golden triangle and golden gnomon (two isosceles triangles whose sides and base are in the golden ratio), [11] the 80-80-20 triangle appearing in the Langley's Adventitious Angles puzzle, [12] and the 30-30-120 triangle of the triakis triangular tiling.
A right star antiprism has two congruent coaxial regular convex or star polygon base faces, and 2n isosceles triangle side faces. Any star antiprism with regular convex or star polygon bases can be made a right star antiprism (by translating and/or twisting one of its bases, if necessary).
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 ...