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A right triangle or right-angled triangle, sometimes called an orthogonal triangle or rectangular triangle, is a triangle in which two sides are perpendicular forming a right angle ( 1⁄4 turn or 90 degrees ). The side opposite to the right angle is called the hypotenuse (side in the figure). The sides adjacent to the right angle are called ...
The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the base, in which case the opposite vertex is called the apex; the shortest segment between base and apex is the height. The area of a triangle equals one half the product of height and base length.
Altitude (triangle) The three altitudes of a triangle intersect at the orthocenter, which for an acute triangle is inside the triangle. In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the side opposite the vertex. This line containing the opposite side is called the extended base ...
In Euclidean geometry, the geometric mean theorem or right triangle altitude theorem is a relation between the altitude on the hypotenuse in a right triangle and the two line segments it creates on the hypotenuse. It states that the geometric mean of the two segments equals the altitude. If h denotes the altitude in a right triangle and p and q ...
In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
The legs of either right triangle formed by an altitude of the equilateral triangle are half of the base , and the hypotenuse is the side of the equilateral triangle. The height of an equilateral triangle can be found using the Pythagorean theorem ( a 2 ) 2 + h 2 = a 2 {\displaystyle \left({\frac {a}{2}}\right)^{2}+h^{2}=a^{2}} so that h = 3 2 ...
Angle-based special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degrees or π 2 radians, is equal to the sum of the other two angles. The side lengths are generally deduced from the basis of the unit ...
Hypotenuse. A right-angled triangle and its hypotenuse. In geometry, a hypotenuse is the side of a right triangle opposite the right angle. [1] It is the longest side of any such triangle; the two other shorter sides of such a triangle are called catheti or legs. The length of the hypotenuse can be found using the Pythagorean theorem, which ...