Axis of symmetry

[duì chèn zhóu]

Mathematical noun

open 2 entries with the same name

Collection

zero Useful+1

zero

This entry is made by Compilation and application of scientific encyclopedia entries of "Science Popularization China" to examine.

Axis of symmetry, a mathematical term, refers to a straight line that makes a geometric figure axisymmetric or rotationally symmetric. When one part of a symmetrical figure rotates a certain angle around it, it coincides with the other part. Many figures have axes of symmetry. for example ellipse 、 hyperbola There are two axes of symmetry, parabola There is one. just cone Or positive cylinder The axis of symmetry of is a straight line passing through the center of the bottom surface and the vertex or the center of another bottom surface.^[1]

Chinese name: Axis of symmetry
Foreign name: axis of symmetry
Discipline: geometry

Definition: Make the graph form an axisymmetric or rotationally symmetric straight line
Example: Square, circle, parabola, hyperbola, etc
Type: Mathematical noun

catalog

definition

Announce

edit

First, introduce the concept of point symmetry about a straight line: if points A and B are in a straight line

On both sides of the, and

Is that of segment AB Vertical bisector , then the weighing points A and B are about the straight line

Symmetric to each other, points A and B are mutually called about straight lines

Of Symmetrical point , straight line

It is called the axis of symmetry.^[2]

Definition I

On the plane, if all points of figure F are about the line on the plane

Axisymmetric, straight

It is called the axis of symmetry under the figure.

Definition II

On the plane, if there is a line

, all points of figure F about lines

A figure made up of symmetrical points. If it is still figure F itself, then figure F is called axisymmetric figure, straight line

Its axis of symmetry.

The three figures in Figure 1 have two, one and four symmetry axes respectively.^[2]

Figure 1

theorem

Announce

edit

① The distance between any point on the symmetry axis and the symmetry point is equal;

② The line segment connected by the symmetry point is vertically bisected by the symmetry axis.

Inference: If two figures are symmetrical about a straight line axis, then these two figures are Congruent figure 。^[2]

Common axisymmetric figures

Announce

edit

Several common axisymmetric and centrosymmetric figures:^[2]

Axisymmetric figure ： line segment 、 horn 、 an isosceles triangle 、 Equilateral triangle 、 diamond 、 rectangle 、 square 、 Isosceles trapezoid 、 circular 、 hyperbola (There are two symmetry axes) ellipse (There are two symmetry axes) parabola (There is a symmetry axis), etc.

Number of symmetrical axes : The angle has one axis of symmetry, that is Angular bisector The straight line; Isosceles triangle has one axis of symmetry, which is the base Vertical bisector ； An equilateral triangle has three axes of symmetry, which are the vertical bisectors on the three sides; The diamond has two symmetry axes, which are the straight lines of two diagonals, and the rectangle has two symmetry axes, which are two sets of opposite sides midpoint A straight line;

Centrosymmetric figure : line segment parallelogram , diamond, rectangle, square, circle, etc.

Symmetrical center : the symmetry center of the line segment is the midpoint of the line segment; The symmetry center of parallelogram, diamond, rectangle and square is diagonal Intersection of; The center of symmetry of a circle is the center of the circle.

Note: Line segment, diamond, rectangle, square and circle are both axisymmetric and centrosymmetric figures.

In coordinate system Axisymmetric transformation Transformation with centrosymmetry:

The coordinates of point P (x, y) with respect to the point P ₁ symmetric about the x axis are (x, - y), and the coordinates of the point P ₂ symmetric about the y axis are (- x, y). The coordinates of the point P3 symmetric about the origin are (- x, - y). This rule can also be recorded as: with respect to the point symmetric about the y axis (x axis) Ordinate (abscissa) same, Abscissa (ordinate) Opposite to each other 。 For a point whose origin is centrosymmetric, the abscissa is the opposite of the original abscissa, and the ordinate is the opposite of the original ordinate, that is, the abscissa and ordinate are multiplied by - 1.^[2]

Novice on the road

Growth task Getting Started with Editing Edit Rule Edit by myself

I have questions

Content query Online Service Official post bar Feedback

Complaints and suggestions

Report bad information Failed to appeal through entries Complaint of infringement information Blocking query and unblocking

Jinggong Network Anbei No. 1100000200001