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Example:Find Angle Measure (Based on Parallel lines)

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, the angle symbol

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle. The magnitude of the angle is the "amount of rotation" that separates the two rays, and can be measured by considering the length of circular arc swept out when one ray is rotated about the vertex to coincide with the other (see "Measuring angles", below). Where there is no possibility of confusion, the term "angle" is used interchangeably for both the geometric configuration itself and for its angular magnitude (which is simply a numerical quantity).




Parallel (geometry)

Parallelism is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. The existence and properties of parallel lines are the basis of Euclid's parallel postulate. Two lines in a plane that do not intersect or meet are called parallel lines.

The parallel symbol is  . For example,  indicates that line AB is parallel to line CD.


As shown by the tick marks, lines a and b are parallel. This can be proved because the transversal t produces congruent angles.




Transversal line

In geometry, a transversal line is a line that passes through two or more other coplanar lines at different points.

In Euclidean geometry if lines a and b are parallel, and line t intersects lines a and b, then corresponding angles formed by line t and the parallel lines are congruent.




Theorem 9 If a transversal intersects two parallel lines, then the alternate interior angles are congruent.

Theorem 12 If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary. (Our solved example in mathguru.com uses this concept)





The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.