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In geometry, Thales's theorem states that if A, B, and C are distinct points on a circle where the line AC is a diameter, the angle ∠ ABC is a right angle. Thales's theorem is a special case of the inscribed angle theorem and is mentioned and proved as part of the 31st proposition in the third book of Euclid 's Elements . [ 1 ]
Antiparallel lines, a congruent but opposite relative orientation of two lines in relation to another line or angle Antiparallel vectors , a pair of vectors pointed in opposite directions Antiparallel (electronics) , the polarity of devices run in parallel
[19]: 14–15 The torque can vanish even when the force is non-zero, if the body is located at the reference point (=) or if the force and the displacement vector are directed along the same line. The angular momentum of a collection of point masses, and thus of an extended body, is found by adding the contributions from each of the points.
The concept of angles between lines (in the plane or in space), between two planes (dihedral angle) or between a line and a plane can be generalized to arbitrary dimensions. This generalization was first discussed by Camille Jordan. [1]
Lines and are antiparallel with respect to the line if they make the same angle with in the opposite senses. Two lines l 1 {\displaystyle l_{1}} and l 2 {\displaystyle l_{2}} are antiparallel with respect to the sides of an angle if they make the same angle ∠ A P C {\displaystyle \angle APC} in the opposite senses with the bisector of that angle.
If not, we may suppose AB < CB' without loss of generality. Let E be a point on the line s on the opposite side of A from C. Take A' on CB' so that A'B' = AB. 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'.
It is the straight line through the point at which the force is applied, and is in the same direction as the vector F →. [1] [2] The concept is essential, for instance, for understanding the net effect of multiple forces applied to a body. For example, if two forces of equal magnitude act upon a rigid body along the same line of action but in ...
The spread between two lines is defined in rational geometry as the square of the sine of the angle between the lines. As the sine of an angle and the sine of its supplementary angle are the same, any angle of rotation that maps one of the lines into the other leads to the same value for the spread between the lines.