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The segment AB is perpendicular to the segment CD because the two angles it creates (indicated in orange and blue) are each 90 degrees. The segment AB can be called the perpendicular from A to the segment CD, using "perpendicular" as a noun. The point B is called the foot of the perpendicular from A to segment CD, or simply, the foot of A on CD ...
The sum of the measures of the angles of any triangle is less than 180° if the geometry is hyperbolic, equal to 180° if the geometry is Euclidean, and greater than 180° if the geometry is elliptic. The defect of a triangle is the numerical value (180° − sum of the measures of the angles of the triangle). This result may also be stated as ...
A right triangle ABC with its right angle at C, hypotenuse c, and legs a and b,. 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).
In a triangle, four basic types of sets of concurrent lines are altitudes, angle bisectors, medians, and perpendicular bisectors: A triangle's altitudes run from each vertex and meet the opposite side at a right angle. The point where the three altitudes meet is the orthocenter.
An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two interior angles that are not adjacent to it; this is the exterior angle theorem. [34]
In an obtuse triangle (one with an obtuse angle), the foot of the altitude to the obtuse-angled vertex falls in the interior of the opposite side, but the feet of the altitudes to the acute-angled vertices fall on the opposite extended side, exterior to the triangle. This is illustrated in the adjacent diagram: in this obtuse triangle, an ...
The line segments AB and CD are perpendicular to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Although many authors use the two terms perpendicular and orthogonal interchangeably, the term perpendicular is more specifically used for lines and planes that intersect to form a right angle, whereas orthogonal is used in generalizations ...
The angles between subspaces satisfy the triangle inequality in terms of majorization and thus can be used to define a distance on the set of all subspaces turning the set into a metric space. [ 8 ] The sine of the angles between subspaces satisfy the triangle inequality in terms of majorization and thus can be used to define a distance on the ...
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