Search results
Results From The WOW.Com Content Network
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one ...
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.
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 ...
A Kepler triangle is a special right triangle with edge lengths in geometric progression. The ratio of the progression is where is the golden ratio, and the progression can be written: , or approximately . Squares on the edges of this triangle have areas in another geometric progression, . Alternative definitions of the same triangle ...
Intercept theorem. The intercept theorem, also known as Thales's theorem, basic proportionality theorem or side splitter theorem, is an important theorem in elementary geometry about the ratios of various line segments that are created if two rays with a common starting point are intercepted by a pair of parallels.
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. Expressed as a mathematical formula, if h denotes the ...
The respective lengths a, b, and c of the sides of these three polygons satisfy the equation a 2 + b 2 = c 2, so line segments with these lengths form a right triangle (by the converse of the Pythagorean theorem). The ratio of the side length of the hexagon to the decagon is the golden ratio, so this triangle forms half of a golden rectangle. [8]
The golden ratio also appears in hyperbolic geometry, as the maximum distance from a point on one side of an ideal triangle to the closer of the other two sides: this distance, the side length of the equilateral triangle formed by the points of tangency of a circle inscribed within the ideal triangle, is (). [67]