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Perpendicular Lines usmam.org Topical overview | Geometry overview | MathBits" Teacher sources Terms the Use contact Person: Donna Roberts

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NOTE: The techniques for proofs that the theorems declared on this web page are "discussed" only. A "formal" proof would need that more details be listed.

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Perpendicular currently (or segments) actually form four ideal angles, even if only among the ideal angles is marked with a box.

The statement above is in reality a theorem i m sorry is discussed further under on this page.

You are watching: If two lines are perpendicular then they form congruent adjacent angles

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There room a pair of usual sense concepts relating come perpendicular lines:


1. The shortest distance from a suggest to a heat is the perpendicular distance. any type of distance, other than the perpendicular distance, from suggest P to heat m will become the hypotenuse the the best triangle. The is known that the hypotenuse the a ideal triangle is the longest next of the triangle.
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2. In a plane, v a suggest not top top a line, there is one, and only one, perpendicular come the line.

See more: Similarities Between Middle Ages And Renaissance Art Similar?


If we assume there room two perpendiculars to heat m from suggest P, us will produce a triangle include two appropriate angles (which is no possible). Our presumption of 2 perpendiculars from allude P is not possible.

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Perpendicular present can additionally be linked to the concept of parallel lines:


3. In a plane, if a line is perpendicular to one of two parallel lines, that is additionally perpendicular to the various other line. In the diagram in ~ the right, if m | | n and tm, then t n. The two significant right angles are equivalent angles for parallel lines, and are thus congruent. Thus, a right angle likewise exists wherein line t intersects line n.
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In the diagram in ~ the right, if tm and sm,then t | | s.Since t and also s room each perpendicular to line m, we have actually two ideal angles wherein the intersections occur. Due to the fact that all appropriate angles are congruent, we have actually congruent equivalent angles which develop parallel lines.


When 2 lines are perpendicular, there are four angles created at the point of intersection. It provides no distinction "where" you label the "box", since every one of the angles are appropriate angles.

By vertical angles, the 2 angles across from one another are the exact same size (both 90º). By using a straight pair, the adjacent angles add to 180º, making any angle adjacent to the box an additional 90º angle.


When two adjacent angles type a straight pair, your non-shared sides form a directly line (m). This tells us that the procedures of the 2 angles will add to 180º. If these two angles likewise happen to be congruent (of same measure), we have two angle of the same size adding to 180º. Each angle will be 90º make m n.
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In the diagram in ~ the left,