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In grammar, parallelism, also known as parallel structure or parallel construction, is a balance within one or more sentences of similar phrases or clauses that have the same grammatical structure. [1] The application of parallelism affects readability and may make texts easier to process. [2]
The repeated sentences or clauses provide emphasis to a central theme or idea the author is trying to convey. [1] Parallelism is the mark of a mature language speaker. [2] In language, syntax is the structure of a sentence, thus parallel syntax can also be called parallel sentence structure. This rhetorical tool improves the flow of a sentence ...
the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line y = − x / m . {\displaystyle y=-x/m\,.} This distance can be found by first solving the linear systems
János Bolyai discovered a construction which gives the asymptotic parallel s to a line r passing through a point A not on r. [1] Drop a perpendicular from A onto B on r. Choose any point C on r different from B. Erect a perpendicular t to r at C. Drop a perpendicular from A onto D on t. Then length DA is longer than CB, but shorter than CA.
Given a line and a point P not on that line, construct a line, t, perpendicular to the given one through the point P, and then a perpendicular to this perpendicular at the point P. This line is parallel because it cannot meet ℓ {\displaystyle \ell } and form a triangle, which is stated in Book 1 Proposition 27 in Euclid's Elements . [ 15 ]
The three perpendicular bisectors meet at the circumcenter. Other sets of lines associated with a triangle are concurrent as well. For example: Any median (which is necessarily a bisector of the triangle's area) is concurrent with two other area bisectors each of which is parallel to a side. [1]
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