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In elementary geometry, the property of being perpendicular (perpendicularity) is the relationship between two lines which meet at a right angle (90 degrees). The property extends to other related geometric objects. A line is said to be perpendicular to another line if the two lines intersect at a right angle. Explicitly, a first line is perpendicular to a second line if (1) the two lines meet; and (2) at the point of intersection the straight angle on one side of the first line is cut by the second line into two congruent angles. Perpendicularity can be shown to be symmetric, meaning if a first line is perpendicular to a second line, then the second line is also perpendicular to the first. For this reason, we may speak of two lines as being perpendicular (to each other) without specifying an order. Perpendicularity easily extends to segments and rays. For example, a line segment is perpendicular to a line segment if, when each is extended in both directions to form an infinite line, these two resulting lines are perpendicular in the sense above. In symbols, means line segment AB is perpendicular to line segment CD. The point ''B'' is called a ''foot of the perpendicular from ''A'' to segment '', or simply, a ''foot of ''A'' on ''. A line is said to be perpendicular to a plane if it is perpendicular to every line in the plane that it intersects. This definition depends on the definition of perpendicularity between lines. Two planes in space are said to be perpendicular if the dihedral angle at which they meet is a right angle (90 degrees). Perpendicularity is one particular instance of the more general mathematical concept of orthogonality; perpendicularity is the orthogonality of classical geometric objects. Thus, in advanced mathematics, the word "perpendicular" is sometimes used to describe much more complicated geometric orthogonality conditions, such as that between a surface and its normal. == Construction of the perpendicular == To make the perpendicular to the line AB through the point P using compass and straightedge, proceed as follows (see figure): * Step 1 (red): construct a circle with center at P to create points A' and B' on the line AB, which are equidistant from P. * Step 2 (green): construct circles centered at A' and B' having equal radius. Let Q and R be the points of intersection of these two circles. * Step 3 (blue): connect Q and R to construct the desired perpendicular PQ. To prove that the PQ is perpendicular to AB, use the SSS congruence theorem for ' and QPB' to conclude that angles OPA' and OPB' are equal. Then use the SAS congruence theorem for triangles OPA' and OPB' to conclude that angles POA and POB are equal. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Perpendicular」の詳細全文を読む スポンサード リンク
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