"Basic Properties of Axisymmetry" PPT Courseware 2

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"Basic Properties of Axisymmetry" PPT Courseware 2

Review and consolidate 1:

1. Axisymmetric properties:

(1) In two figures that are axially symmetrical, the line connecting the corresponding points is bisected perpendicularly by the axis of symmetry,

(2) Two axially symmetric figures are congruent.

(3) Corresponding line segments are equal and corresponding angles are equal.

(4) In two figures that are axially symmetrical, the intersection of the straight lines of the symmetrical line segments is on the axis of symmetry or the straight lines of the symmetrical line segments are parallel to each other.

(5) In two axially symmetric figures, the lines connecting the symmetry points are parallel to each other or on the same straight line.

Review and consolidation 2:

2. Steps to draw a polygon that is axially symmetric about a straight line:

(1). Draw the symmetry points of the key points in the graph,

(2). Connect each symmetry point in sequence.

Note: Keep the dotted lines.

Cooperation and exchange

1. As shown in the figure, there is a rectangle ABCD in the plane Cartesian coordinate system:

(1) If point A and point B are symmetrical about the X-axis, what are the coordinates of point B? Point C and point D are symmetrical about the X axis. What are the coordinates of point D?

(2) What are the characteristics of the coordinates of a point that is symmetrical about the x-axis?

Points that are symmetrical about the x-axis have the same abscissas and opposite ordinates.

Summary: The characteristics of the coordinates of a point that is symmetrical about the X-axis are: the abscissas are the same, and the ordinates are opposite numbers to each other.

(abbreviation: horizontal same vertical reverse)

practise:

1. Point P(-4, 7) and point Q are symmetrical about the x-axis, then the coordinates of point Q are __________.

2. Point M (a, -5) and point N (-2, b) are symmetrical about the X axis, then a=_____, b =_____.

(1) What is the positional relationship between point A and point D? What about point B and point C?

Point A and point D are symmetrical about the y-axis, and point B and point C are symmetrical about the y-axis;

(2) What are the characteristics of the coordinates of a point that is symmetric about the y-axis?

The abscissas of points that are symmetrical about the y-axis are opposite numbers and the ordinates are the same.

Summary: The characteristics of the coordinates of a point that is symmetrical about the y-axis are: the abscissas are opposite numbers to each other, and the ordinates are equal.

(abbreviation: horizontal reverse vertical same)

practise:

1. Point P(-5, 6) and point Q are symmetrical about the y-axis, then the coordinates of point Q are __________.

2. Point M (a, -5) and point N (-2, b) are symmetrical about the y-axis, then a=_____, b =_____.

Summary of new knowledge

Coordinate characteristics of "point symmetric about coordinate axis":

(1) The coordinates of the point that is symmetrical about the x-axis: the same as the transverse direction and the opposite direction as the vertical direction;

(2) The coordinates of a point that is symmetrical about the y-axis: the same as the horizontal and vertical directions.

In the rectangular coordinate system,

The symmetry point of point (a, b) about the X-axis is (a,-b)

The symmetry point of point (a, b) about the Y axis is (-a, b)

practise:

1. Point P(-5, 6) and point Q are symmetrical about the x-axis, then the coordinates of point Q are __________.

2. Point M (a, -5) and point N (-2, b) are symmetrical about the x-axis, then a=_____, b =_____.

3. Point P(-5, 6) and point Q are symmetrical about the y-axis, then the coordinates of point Q are __________.

4. Point M (a, -5) and point N (-2, b) are symmetrical about the y-axis, then a=_____, b =_____.

5. Point P(2a+b,-3a) and point Q(8,b+2) are known.

If point p and point Q are symmetrical about the x-axis, then a=_____ b=_______.

If point p and point Q are symmetrical about the y-axis, then a=_____ b=_______.

6. Keep the abscissa coordinates of each point of a figure in the plane rectangular coordinate system unchanged, and multiply the ordinates by -1. The resulting figure will be the same as the original figure (A)

A is symmetrical about the X-axis. B is symmetrical about the Y-axis

C is symmetric about the origin D cannot be determined

7. The relationship between point A(-3,2) and point B(-3,-2) is (　)

A is symmetrical about the X-axis; B is symmetrical about the Y-axis

C. Symmetry about the origin. D. All of the above are incorrect.

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"Basic Properties of Axisymmetry" PPT courseware 3:

"Basic Properties of Axial Symmetry" PPT Courseware 3 Teaching Objectives 1. Experience the process of exploring the properties of two axially symmetrical figures, further experience the characteristics of axial symmetry, and develop spatial concepts. 2. Develop the habit of diligent thinking through hands-on operations, cooperation and communication. Activity..

"Basic Properties of Axisymmetry" PPT courseware:

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Update Time: 2024-06-28

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