Perpendicular

In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects.

A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order.

Perpendicularity easily extends to segments and rays. For example, a line segment is perpendicular to a line segment if, when each is extended in both directions to form an infinite line, these two resulting lines are perpendicular in the sense above. In symbols, means line segment AB is perpendicular to line segment CD. The point B is called a foot of the perpendicular from A to segment , or simply, a foot of A on .

Right angle

In geometry and trigonometry, a right angle is an angle that bisects the angle formed by two adjacent parts of a straight line. More precisely, if a ray is placed so that its endpoint is on a line and the adjacent angles are equal, then they are right angles. As a rotation, a right angle corresponds to a quarter turn (that is, a quarter of a full circle).

Closely related and important geometrical concepts are perpendicular lines, meaning lines that form right angles at their point of intersection, and orthogonality, which is the property of forming right angles, usually applied to vectors. The presence of a right angle in a triangle is the defining factor for right triangles, making the right angle basic to trigonometry.

The term is a calque of Latin angulus rectus; here rectus means "upright", referring to the vertical perpendicular to a horizontal base line.

Symbols

In Unicode, the symbol for a right angle is U+221F ∟ RIGHT ANGLE (HTML ∟).

In diagrams the fact that an angle is a right angle is usually expressed by adding a small right angle that forms a square with the angle in the diagram, as seen in the diagram of a right triangle (in British English, a right-angled triangle) to the right. The symbol for a measured angle, an arc with a dot, is used in some European countries, including German-speaking countries and Poland, as an alternative symbol for a right angle.

Parallel (geometry)

In geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. By extension, a line and a plane, or two planes, in three-dimensional Euclidean space that do not share a point are said to be parallel. However, two lines in three-dimensional space which do not meet must be in a common plane to be considered parallel; otherwise they are called skew lines. Parallel planes are planes in the same three-dimensional space that never meet.

Parallel lines are the subject of Euclid's parallel postulate. Parallelism is primarily a property of affine geometries and Euclidean space is a special instance of this type of geometry. Some other spaces, such as hyperbolic space, have analogous properties that are sometimes referred to as parallelism.

Symbol

The parallel symbol is . For example, indicates that line AB is parallel to line CD.

In the Unicode character set, the "parallel" and "not parallel" signs have codepoints U+2225 (∥) and U+2226 (∦), respectively. In addition, U+22D5 (⋕) represents the relation "equal and parallel to".

Gangs of Wasseypur

Gangs of Wasseypur (stylised as Gangs of वासेपुर) is a 2012 Indian two-part crime film co-written, produced and directed by Anurag Kashyap. Centered on the coal mafia of Dhanbad, and the underlying power struggles, politics and vengeance between three crime families, the Part 1 features ensemble cast with Manoj Bajpai, Nawazuddin Siddiqui, Huma Qureshi, Richa Chadda, Tigmanshu Dhulia in the major roles and its story spans from the early 1940s to mid-1990s. Both parts were originally shot as a single film measuring a total of 319 minutes and screened at the 2012 Cannes Directors' Fortnight but since no Indian theatre would volunteer to screen a five plus hour film, it was divided into two parts for the Indian market.

Cast