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The tangent to a triangle's circumcircle at a vertex is antiparallel to the opposite side. The radius of the circumcircle at a vertex is perpendicular to all lines antiparallel to the opposite sides. red angles are of equal size, ED and the tangent in B are antiparallel to AC and are perpendicular to MB
Transverse – intersecting at any angle, i.e. not parallel. Orthogonal (or perpendicular) – at a right angle (at the point of intersection). Elevation – along a curve from a point on the horizon to the zenith, directly overhead. Depression – along a curve from a point on the horizon to the nadir, directly below.
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 ...
Another common definition uses a human body, standing upright, as a frame of reference. In that case, up is defined as the direction from feet to head, perpendicular to the surface of the Earth. In most cases, up is a directionally oriented position generally opposite to that of the pull of gravity. This statue holds a sword in its proper right ...
The line segments AB and CD are orthogonal to each other. In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.Whereas perpendicular is typically followed by to when relating two lines to one another (e.g., "line A is perpendicular to line B"), [1] orthogonal is commonly used without to (e.g., "orthogonal lines A and B").
Through A' draw a line s' (A'E') on the side closer to E, so that the angle B'A'E' is the same as angle BAE. Then s' meets s in an ordinary point D'. Construct a point D on ray AE so that AD = A'D'. Then D' ≠ D. They are the same distance from r and both lie on s. So the perpendicular bisector of D'D (a segment of s) is also perpendicular to ...
The scalar projection is defined as [2] = ‖ ‖ = ^ where the operator ⋅ denotes a dot product, ‖a‖ is the length of a, and θ is the angle between a and b. The scalar projection is equal in absolute value to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of b ...
Through any point P in the plane, there is one and only one vertical line within the plane and one and only one horizontal line within the plane. This symmetry breaks down as one moves to the three-dimensional case. A vertical line is any line parallel to the vertical direction. A horizontal line is any line normal to a vertical line.