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# Right triangle

A right triangle (American English) or right-angled triangle (British English) is a triangle in which one angle is a right angle (that is, a 90-degree angle). [1]

## Acute and obtuse triangles

An acute triangle is a triangle with all three angles acute (less than 90°).

## Altitude (triangle)

In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex).

## American English

American English (AmE, AE, AmEng, USEng, en-US), sometimes called United States English or U.S. English, is the set of varieties of the English language native to the United States.

## Angle

In plane 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.

## Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

## Arithmetic mean

In mathematics and statistics, the arithmetic mean (stress on third syllable of "arithmetic"), or simply the mean or average when the context is clear, is the sum of a collection of numbers divided by the number of numbers in the collection.

## British English

British English is the standard dialect of English language as spoken and written in the United Kingdom.

## Cathetus

In a right triangle, a cathetus (originally from the Greek word Κάθετος; plural: catheti), commonly known as a leg, is either of the sides that are adjacent to the right angle.

## Circumscribed circle

In geometry, the circumscribed circle or circumcircle of a polygon is a circle which passes through all the vertices of the polygon.

## Degree (angle)

A degree (in full, a degree of arc, arc degree, or arcdegree), usually denoted by ° (the degree symbol), is a measurement of a plane angle, defined so that a full rotation is 360 degrees.

## Diameter

In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.

## Euler line

In geometry, the Euler line, named after Leonhard Euler, is a line determined from any triangle that is not equilateral.

## Geometric mean

In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum).

## Geometric mean theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the lengths of the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse.

## Geometric progression

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

## Golden ratio

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities.

## Harmonic mean

In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means.

## Hyperbolic function

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions.

## Hyperbolic sector

A hyperbolic sector is a region of the Cartesian plane bounded by rays from the origin to two points (a, 1/a) and (b, 1/b) and by the rectangular hyperbola xy.

## Hypotenuse

In geometry, a hypotenuse (rarely: hypothenuse) is the longest side of a right-angled triangle, the side opposite of the right angle.

## If and only if

In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.

## Incircle and excircles of a triangle

In geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.

## Kepler triangle

A Kepler triangle is a right triangle with edge lengths in geometric progression.

## Line segment

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints.

## Mathematics Magazine

Mathematics Magazine is a refereed bimonthly publication of the Mathematical Association of America.

## Median (geometry)

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposing side, bisecting it.

## Midpoint

In geometry, the midpoint is the middle point of a line segment.

## Nine-point circle

In geometry, the nine-point circle is a circle that can be constructed for any given triangle.

## Pythagorean theorem

In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

## Pythagorean triple

A Pythagorean triple consists of three positive integers,, and, such that.

## Right angle

In geometry and trigonometry, a right angle is an angle of exactly 90° (degrees), corresponding to a quarter turn.

## Semicircle

In mathematics (and more specifically geometry), a semicircle is a one-dimensional locus of points that forms half of a circle.

## Semiperimeter

In geometry, the semiperimeter of a polygon is half its perimeter.

## Similarity (geometry)

Two geometrical objects are called similar if they both have the same shape, or one has the same shape as the mirror image of the other.

## Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

## Tangent

In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point.

## Thales's theorem

In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line is a diameter, then the angle ∠ABC is a right angle.

## The Mathematical Gazette

The Mathematical Gazette is an academic journal of mathematics education, published three times yearly, that publishes "articles about the teaching and learning of mathematics with a focus on the 15–20 age range and expositions of attractive areas of mathematics." It was established in 1894 by Edward Mann Langley as the successor to the Reports of the Association for the Improvement of Geometrical Teaching.

## Triangle

A triangle is a polygon with three edges and three vertices.

## Trigonometric functions

In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle.

## Trigonometry

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a branch of mathematics that studies relationships involving lengths and angles of triangles.

## References

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