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assistant Lines snucongo.org Topical outline | Geometry rundown | MathBits" Teacher resources Terms the Use contact Person: Donna Roberts


In geometry, it may be vital to add a heat or segment to a chart to aid in fixing a problem or prove a concept. Such an included line or segment is referred to as an assistant line. Words "auxiliary" way providing added help or support.

You are watching: What is an auxiliary line in geometry

While the is never acceptable to adjust any that the original parts that a diagram, it is acceptable to add new lines or segments. These brand-new lines are attracted "dashed" or "dotted" to indicated that they to be not part of the original diagram.

Auxiliary present are frequently used to produce a triangle in a chart or to develop two congruent triangle in a diagram. Her goal is to include something to the diagram that will help you resolve the problem.


There are a series of postulates the are provided to support the enhancement of an assistant line come a proof, such as:
Through a point not ~ above a heat (segment), only one line deserve to be attracted parallel to the provided line (segment). (Parallel Postulate)
Through a suggest not on a line (segment), only one line can be attracted perpendicular to the offered line (segment).
Through a allude not on a segment, just one heat (segment) deserve to be attracted to the midpoint the the offered segment.
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The trouble at the left wants us to prove the the base angles of one isosceles triangle room congruent. As you deserve to see, over there is not much for united state to occupational with in the diagram.

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The assistant segment offers us 2 triangles v which come work.


If we include an auxiliary line i beg your pardon is a perpendicular come the basic from point B, us can form two ideal triangles in which come work. We deserve to then job-related our method toward obtaining the angles to be congruent as matching parts of congruent triangles.

Always include an auxiliary line in the simplest way possible. Perform not include a multitude of auxiliary lines and also make a confusing mess of the diagram.

See more: 51 Is 17 Percent Of What Number Is 140? 17 Is What Percent Of 51

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Be sure that the problems that you place on an assistant line space actually true.


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Given the diagram at the left, a college student draws an auxiliary segment from suggest D to point A developing a second triangle. The student says that the "Reason" for the auxiliary line is that "through a suggest not ~ above a line (segment), just one line can be attracted perpendicular to the provided line (segment)" and also states the
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. WRONG!

We have no way of discovering that the perpendicular native A to will intersect at allude D. It will more likely crossing somewhere between allude C and allude D. The student can draw the segment native A come D, stating that 2 points identify one distinctive line, but the college student cannot state the the segment is perpendicular come at D.


Topical summary | Geometry overview | snucongo.org | MathBits" Teacher sources Terms the Use contact Person: Donna Roberts