Perpendicular

src: i.ytimg.com

In basic geometry, property becomes perpendicular ( perpendicular ) is the relationship between two lines that meet at right angles (90 degrees). The property extends to other related geometric objects.

A line is said to be perpendicular to another line if both lines intersect at the right angle. Explicitly, the first line is perpendicular to the second line if (1) the two lines meet; and (2) at the point of intersection of the straight angle on one side of the first line cut by the second line into two congruent angles. Upright perpendicular can be shown to be symmetrical, which means that if the first line is perpendicular to the second line, then the second line is also perpendicular to the first. For this reason, we can talk about two lines as perpendicular (to each other) without specifying the order.

Tegak lurus dengan mudah meluas ke segmen dan sinar. Misalnya, segmen garis ${\ displaystyle {\ overline {AB}}}  ÂÂ$ tegak lurus dengan segmen garis ${\ displaystyle {\ overline {CD}}}  ÂÂ$ jika, ketika masing-masing diperpanjang di kedua arah untuk membentuk garis tak terbatas, dua garis yang dihasilkan ini tegak lurus dalam arti di atas. Dalam simbol, ${\ displaystyle {\ overline {AB}} \ pen {\ overline {CD}}}  ÂÂ$ berarti ruas garis AB tegak lurus terhadap ruas garis segmen. Untuk informasi mengenai simbol tegak lurus, lihat Up tack.

A line is said to be perpendicular to the plane if perpendicular to each line in the truncated area. This definition depends on the definition of perpendicular between lines.

Two planes in space are said to be perpendicular if the dihedral angle in which they meet is a right angle (90 degrees).

Upright perpendicular is one particular example of a more general concept of orthogonal mathematics; perpendicular is the orthogonality of a classical geometric object. Thus, in advanced mathematics, the word "perpendicular" is sometimes used to describe much more complicated geometric orthogonality conditions, such as between surface and normal.

Video Perpendicular

Legs perpendicular

The word foot is often used in connection with perpendiculars. This usage is exemplified in the above diagram, above, and caption. The diagram can be in any orientation. The foot is not necessarily at the bottom.

More precisely, let A be the point and m a line. If B is the intersection point m and the unique line through A that is perpendicular to m , then B is called this foot perpendicular through A .

Maps Perpendicular

Straight construction

To make a line perpendicular to AB through point P using compass and straight line construction, do the following (see left image):

• Step 1 (red): create circle with center in P to make point A 'and B' on line AB, equidistant from P.
• Step 2 (green): create a circle centered on A 'and B' with the same radius. Let Q and R be the intersection of these two circles.
• Step 3 (blue): connect Q and R to make the desired perpendicular PQ.

To prove that PQ is perpendicular to AB, use the SSS conformity theorem for 'and QPB' to conclude that the angles of OPA 'and OPB' are the same. Then use the SAS congruency theorem for the OPA 'and OPB' triangles to conclude that the POA and POB angles are the same.

To make a line perpendicular to the line g on or through point P using Thales's theorem, see the animation on the right.

The Pythagoras theorem can be used as a basis for the method of building right angles. For example, by counting links, three chains can be made with lengths in the 3: 4: 5 ratio. These can be arranged to form triangles, which will have a right angle on the longest side. This method is useful for placing gardens and fields, where large dimensions, and high accuracy are not required. Chains can be used repeatedly whenever needed.

src: www.cpalms.org

In relation to parallel lines

If two lines ( a and b ) are both perpendicular to the third line ( c ), all angles formed along the third line are the right angles. Therefore, in the Euclidean geometry, every two lines perpendicular to the third line align with each other, because parallel postulas. On the other hand, if one line perpendicular to the second line, this line is also perpendicular to the line corresponding to the second line.

In the picture on the right, all the shaded corners are orange in one another and all the green shaded corners are congruent with each other, since the vertical angle is the congruent and alternating interior angles formed by the parallel lines of transverse cuts. congruent. Therefore, if the lines a and b are parallel, one of the following conclusions leads to everything else:

• One corner of the diagram is a right angle.
• One of the shaded corners of orange is the same as one of the green shaded corners.
• The line c is perpendicular to the line a .
• The line c is perpendicular to the line b .

src: i.ytimg.com

In computing distance

Distance from point to line is the distance to the nearest point on the line. That is the point where the segment from it to the given point is perpendicular to the line.

Likewise, the distance from point to curve is measured by a line segment perpendicular to the tangent to the curve at the nearest point on the curve.

Regression is perpendicular to the line to the data point by minimizing the amount of perpendicular distance from the data point to the line.

Distance from point to plane is measured as the length of the point along the segment perpendicular to the plane, which means that the line is perpendicular to all the lines on the plane passing the nearest point on the plane to the specified point.

src: i.ytimg.com

Graph function

In a two-dimensional plane, the right angle can be formed by two intersecting lines if the slope product is equal to -1. Thus defining two linear functions: y ₁ = a ₁ x b ₁ and y ₂ = a 2 , the function graph will be perpendicular and will make the right four corners where line intersects if a ₁ a ₂ = -1 . However, this method can not be used if the slope is zero or undefined (line parallel to the axis).

For other methods, allow two linear functions to be: a ₁ x y c ₁ = 0 and a ₂ > b ₂ y c ₂ = 0. The line will be perpendicular if and only if a ₁ a ₂ 1 b ₂ = 0. This method is simplified from a point (or, more generally, in-product) product of a vector. In particular, two vectors are considered orthogonal if the product in them is zero.

src: i.ytimg.com

In other circles and conics

Circles

Each diameter of the circle is perpendicular to the tangent to the circle at the point where the diameter intersects the circle.

The line segment through the center of the circle divides the two chords perpendicular to the chord.

If the intersections of two perpendicular chords divide one chord into length a and b and divide the other chord into length c and d , then a ² b ² c ² d ² equals the diameter of the diameter.

The sum of the squared lengths of the two perpendicular chords that cut at a certain point is equal to the mutually perpendicular chord that cuts at the same point, and given by 8 r ² - 4 p ² (where r is the radius of the circle and p is the distance from the center point to the intersection point).

Thales's theorem states that the two lines both go through the same point on a circle but pass opposite the opposite ends of the vertical. This is equivalent to saying that every diameter of a circle combines a right angle at any point in a circle, except for the two end points of the diameter.

Ellipse

The major and minor axes of the ellipse are perpendicular to each other and with the tangent to the ellipse at the points where the axis intersects the ellipse.

The main axis of the ellipse is perpendicular to the directrix and any latus rectus.

Parabolas

In a parabola, the axis of symmetry is perpendicular to each rectum, directrix, and tangent latitude at the point where the axis intersects the parabola.

From the point on the tangent line to the top of the parabola, the other tangent line to the parabola is perpendicular to the line from that point through the focus of the parabola.

The orthoptic property of the parabola is that If two tangents to a parabola are perpendicular to each other, then they intersect on directrix. In contrast, two tangents intersect on directrix perpendicular. This implies that, judging from any point on the directrix, any parabola has a right angle.

Hiperbole

The transverse axis of the hyperbola is perpendicular to the conjugate axis and to each of the directrix.

The product of perpendicular distance from point P to hyperbola or to conjugate hyperbola to asymptotes is independent constant from location P.

Hiperbola persegi panjang memiliki asimtot yang tegak lurus satu sama lain. Ini memiliki eksentrisitas yang sama dengan ${\ displaystyle {\ sqrt {2}}.}  ÂÂ$

src: saylordotorg.github.io

Dalam poligon

Segitiga

The legs of the right triangle are perpendicular to each other.

The height of the triangle is perpendicular to each base. Bisectors perpendicular from the side also play an important role in the geometry of the triangle.

The Euler line of an equilateral triangle is perpendicular to the base of the triangle.

The Droz-Farny line theorem concerns the property of two perpendicular lines intersecting on an orthocenter triangle.

Harcourt's theorem discusses the relationship of line segments through a point and perpendicular to the line tangent to the triangular circle.

Quadrilateral

In a square or other rectangle, all adjacent side pairs are perpendicular. The right trapezoid is a trapezoid that has two pairs of adjacent sides that are perpendicular.

Each of the four maltitudes of the quadrilateral is perpendicular to the side through the opposite center point of the side.

An orthodiagonal rectangle is a diagonal rectangle perpendicular. These include the square, rhubarb, and kites. With the Brahmagupta theorem, in the cortical ortodiagonal square, the line through the one-sided center point and through the intersection point of the diagonal is perpendicular to the opposite side.

With van Aubel's theorem, if the square is built externally on the sides of a rectangle, the line segments connecting the opposite box centers are perpendicular and equal in length.

src: d1avenlh0i1xmr.cloudfront.net

Rows in three dimensions

Up to three lines in three-dimensional space can be paired perpendicularly, as exemplified by the axes x, y , and z of the three-dimensional Cartesian coordinate system.

src: showme0-9071.kxcdn.com

See also

• Tangential and normal components

src: www.cpalms.org

Note

src: d1avenlh0i1xmr.cloudfront.net

References

• Altshiller-Court, Nathan (1925), College Geometry: Introduction to Modern Triangle and Circle Geometry (2nd ed.), New York: Barnes & amp; Noble, LCCNÃ, 52-13504 Ã,
Kay, David C. (1969), College Geometry , New York: Holt, Rinehart and Winston, LCCNÃ, 69-12075

src: i.ytimg.com

External links

• Definition: perpendicular to the interactive animation.
• How to draw line-line with compass and straight edge (animated demonstration).
• How to draw perpendicular to the endpoint of the ray with compass and straight edge (animated demonstration).

Source of the article : Wikipedia