Isosceles triangle in the context of "Transformation geometry"

In geometry, an apex (pl.: apices) is the vertex which is in some sense the "highest" of the figure to which it belongs. The term is typically used to refer to the vertex opposite from some "base". The word is derived from the Latin for 'summit, peak, tip, top, extreme end'. The term apex may be used in different contexts:

• In an isosceles triangle, the apex is the vertex where the two sides of equal length meet, opposite the unequal third side.

A trestle bridge is a bridge composed of a number of short spans supported by closely spaced frames usually carrying a railroad line. A trestle (sometimes tressel) is a rigid frame used as a support, historically a tripod used to support a stool or a pair of isosceles triangles joined at their apices by a plank or beam such as the support structure for a trestle table. Each supporting frame is a bent. A trestle differs from a viaduct in that viaducts have towers that support much longer spans and typically have a higher elevation.

Timber and iron trestles (i.e. bridges) were extensively used in the 19th century, the former making up from 1 to 3 percent of the total length of the average railroad. In the 21st century, steel and sometimes concrete trestles are commonly used to bridge particularly deep valleys, while timber trestles remain common in certain areas.

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. This means that either object can be rescaled, repositioned, and reflected, so as to coincide precisely with the other object. If two objects are similar, each is congruent to the result of a particular uniform scaling of the other.

For example, all circles are similar to each other, all squares are similar to each other, and all equilateral triangles are similar to each other. On the other hand, ellipses are not all similar to each other, rectangles are not all similar to each other, and isosceles triangles are not all similar to each other. This is because two ellipses can have different width to height ratios, two rectangles can have different length to breadth ratios, and two isosceles triangles can have different base angles.

An equilateral triangle is a triangle in which all three sides have the same length, and all three angles are equal. Because of these properties, the equilateral triangle is a regular polygon, occasionally known as the regular triangle. It is the special case of an isosceles triangle by modern definition, creating more special properties.

The equilateral triangle can be found in various tilings, and in polyhedrons such as the deltahedron and antiprism. It appears in real life in popular culture, architecture, and the study of stereochemistry resembling the molecular known as the trigonal planar molecular geometry.

In structural engineering, a trestle support (or simply trestle) is a structural element with rigid beams forming the equal sides of two parallel isosceles triangles, joined at their apices by a plank or beam. Sometimes additional rungs are stretched between the two beams. A pair of trestle legs can support one or several boards or planks, forming a trestle table or trestle desk. A network of trestle supports can serve as the framework for a trestle bridge, and a trestle of appropriate size to hold wood for sawing is known as a sawhorse.

The Winter Triangle is an astronomical asterism formed from three of the brightest stars in the winter sky. It is an imaginary isosceles triangle drawn on the celestial sphere, with its defining vertices at Sirius, Betelgeuse, and Procyon, the primary stars in the three constellations of Canis Major, Orion, and Canis Minor, respectively.

Cetonia aurata, called the rose chafer or the green rose chafer, is a beetle, 20 millimetres (3⁄4 in) long, that has a metallic structurally coloured green and a distinct V-shaped scutellum. The scutellum is the small V-shaped area between the wing cases; it may show several small, irregular, white lines and marks. The underside of the beetle has a coppery colour, and its upper side is sometimes bronze, copper, violet, blue/black, or grey.

Cetonia aurata should not be confused with the North American rose chafer, Macrodactylus subspinosus, or with the rarely seen noble chafer, Gnorimus nobilis, which is very similar to the rose chafer. One way to identify Cetonia aurata is to look at its scutellum; on the noble chafer the scutellum is an equilateral triangle, but on the rose chafer it is an isosceles triangle.