Congruence (geometry)

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. 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 translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if we can cut them out and then match them up completely. Turning the paper over is permitted.

In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects.

Side

Side (Greek: Σίδη) is an ancient Greek city on the southern Mediterranean coast of Turkey, a resort town and one of the best-known classical sites in the country. It lies near Manavgat and the village of Selimiye, 78 km from Antalya in the province of Antalya.

It is located on the eastern part of the Pamphylian coast, which lies about 20 km east of the mouth of the Eurymedon River. Today, as in antiquity, the ancient city is situated on a small north-south peninsula about 1 km long and 400 m across.

History

Strabo and Arrian both record that Side was founded by Greek settlers from Cyme in Aeolis, a region of western Anatolia. This most likely occurred in the 7th century BC. Its tutelary deity was Athena, whose head adorned its coinage.

Dating from the tenth century B.C., its coinage bore the head of Athena (Minerva), the patroness of the city, with a legend. Its people, a piratical horde, quickly forgot their own language to adopt that of the aborigines.

Possessing a good harbour for small-craft boats, Side's natural geography made it one of the most important places in Pamphylia and one of the most important trade centres in the region. According to Arrian, when settlers from Cyme came to Side, they could not understand the dialect. After a short while, the influence of this indigenous tongue was so great that the newcomers forgot their native Greek and started using the language of Side. Excavations have revealed several inscriptions written in this language. The inscriptions, dating from the 3rd and 2nd centuries BC, remain undeciphered, but testify that the local language was still in use several centuries after colonisation. Another object found in the excavations at Side, a basalt column base from the 7th century BC and attributable to the Neo-Hittites, provides further evidence of the site's early history. The name Side may be Anatolian in origin, meaning pomegranate.

The Unit (season 3)

The third season of The Unit started on September 25, 2007, with a hiatus, which ended in the season being cut short, occurring after the 11th episode due to 2007–2008 Writers Guild of America strike.

Cast and characters

Main cast

Supporting cast

Recurring cast

Episode list

Notes

References

External links

Angle

In planar geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in a plane, but this plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in Euclidean and other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined by the tangent rays at the point of intersection. Similar statements hold in space, for example, the spherical angle formed by two great circles on a sphere is the dihedral angle between the planes determined by the great circles.

Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is centered at the vertex and delimited by the sides. In the case of a rotation, the arc is centered at the center of the rotation and delimited by any other point and its image by the rotation.

Hong Kong

Hong Kong (香港; "Fragrant Harbour"), officially Hong Kong Special Administrative Region of the People's Republic of China, is an autonomous territory on the southern coast of China at the Pearl River Estuary and the South China Sea. Hong Kong is known for its skyline and deep natural harbour. It has a land area of 1104 km² and shares its northern border with Guangdong Province of Mainland China. With around 7.2 million inhabitants of various nationalities, Hong Kong is one of the world's most densely populated metropolises.

After the First Opium War (1839–42), Hong Kong became a British colony with the perpetual cession of Hong Kong Island, followed by Kowloon Peninsula in 1860 and a 99-year lease of the New Territories from 1898. Hong Kong remained under British control for about a century until the Second World War, when Japan occupied the colony from December 1941 to August 1945. After the Surrender of Japan, the British resumed control. In the 1980s, negotiations between the United Kingdom and the China resulted in the 1984 Sino-British Joint Declaration, which provided for the transfer of sovereignty of Hong Kong on 30 June 1997. The territory became a special administrative region of China with a high degree of autonomy on 1 July 1997 under the principle of one country, two systems. Disputes over the perceived misapplication of this principle have contributed to popular protests, including the 2014 Umbrella Revolution.