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"Exploring the Nature of Axisymmetry" Axisymmetric PPT Teaching Courseware in Life
Part One: Learning Objectives
1. Explore and master the properties of axial symmetry. (Key points)
2. Be able to use the properties of axial symmetry to create symmetrical points, symmetrical figures, symmetrical axes, etc. (Difficulty)
Exploring the properties of axial symmetry PPT, part 2: knowledge review
1. Axisymmetric figures: If a figure is folded in half along a straight line and the parts on both sides of the straight line can completely overlap, then the figure is called an axially symmetric figure. This straight line is called the axis of symmetry of the figure.
2. Axial symmetry: For two figures, fold one figure in half along a certain straight line. If it can completely coincide with the other figure, then the two figures are said to be axially symmetrical. This straight line is the axis of symmetry.
Exploring the properties of axial symmetry PPT, the third part: knowledge explanation
As shown in the picture: Fold a rectangular piece of paper in half, then poke the number "14" with the tip of a pen, open the paper and lay it flat:
(1) What is the relationship between two "14"?
(2) Suppose the straight line where the crease is located is l, what is the relationship between the line segment connecting points E and E′ and l? What about points F and F′?
(3) What is the relationship between line segments AB and A′B′, CD and C′D′?
(4) What is the relationship between ∠1 and ∠2? What about ∠3 and ∠4?
Do it
The picture on the right is an axisymmetric figure:
(1) Find its axis of symmetry.
(2) What is the relationship between the line segment connecting point A and point A1 and the axis of symmetry? What about the line segment connecting point B and point B1?
(3) What is the relationship between line segment AD and line segment A1D1? What about line segments BC and B1C1? Why?
(4) What is the relationship between ∠1 and ∠2? What about ∠3 and ∠4? Tell me your reasons?
Thinking: Based on the above questions, what conclusion can you draw?
Summary
Axisymmetric properties
In an axially symmetrical figure or two axially symmetrical figures, the line segments connected to corresponding points are bisected perpendicularly by the axis of symmetry, the corresponding line segments are equal, and the corresponding angles are equal.
Exploring the properties of axial symmetry PPT, part 4: explanation of examples
Example 1 Draw the symmetrical figure of △ABC about the straight line l.
Method summary: First determine some special points, then make symmetry points of these special points and connect them in sequence.
Example 2 As shown in the figure, the shape of a paraglider is an axially symmetrical quadrilateral ABCD, where ∠BAD=150°, ∠B=40°, then the degree of ∠BCD is ()
A. 130°B. 150°
C． 40° D. 65°
Example 3 As shown in the picture, the side length of square ABCD is 4cm, then the area of the shaded part in the picture is ()
A. 4cm2
B． 8cm2
C． 12cm2
D． 16cm2
Method summary: A square is an axially symmetrical figure. When finding the area of an irregular shaded part in an axially symmetrical figure, you can generally use axially symmetric transformation to convert it into a regular figure and then calculate it.
Exploring the properties of axial symmetry PPT, part 5: in-class training
1. If two figures are symmetrical about a straight line, then the line segments connecting the corresponding points are bisected perpendicularly by __________.
2. The figure below is an axially symmetrical figure. The equal line segments are ____________________ and the equal angles are __________.
3. As shown in the figure, △ABC and △A1B1C1 are symmetrical about the straight line l, then ∠B is ______.
Analysis: From the properties of axial symmetry, we can get ∠A1=∠A=50°, ∠C=∠C1=30°, so ∠B=∠B1=180°-50°-30°=100°.
4. Only half of the two axisymmetric figures below are drawn. Please draw their other half (the straight line L is the axis of symmetry).
Exploring the properties of axial symmetry PPT, part six: expansion and improvement
1. As shown in the figure, it is known that points A and B are two points on the same side of the straight line MN. Points A1 and A are symmetrical about the straight line MN. Connect A1B and the straight line MN to point P to connect AP.
(1) If A1B=5cm, then the length of AP+BP is _______.
(2) In order to solve the drinking water problem of Zhangjia Village A and Lijia Village B within its jurisdiction, a township decided to open a gap P on the side of the river MN to introduce the river water to Zhangjia Village A and Lijia Village B. In order to save money, the built The water channel is the shortest. Where should the gap P be built? Please use the knowledge you have learned to solve this problem and draw the water channel with a red line segment.
2. As shown in the figure, it is known that point P is any point within ∠AOB, point P1, P is symmetrical about OA, point P2, P is symmetrical about OB. Connect P1P2, intersect OA, OB with C, D. Connect PC, PD. If P1P2=10cm, then the perimeter of △PCD is _____.
Exploring the properties of axial symmetry PPT, Part 7: Class summary
Axisymmetric properties
1. The line segments connected to corresponding points are bisected perpendicularly by the axis of symmetry
2. Corresponding line segments are equal and corresponding angles are equal.
Exploring the properties of axial symmetry PPT, part 8: detection in class
1. As shown in the figure, in the field grid composed of four small squares, the vertices of △ABC are all the vertices of the small squares. Draw a triangle that is axially symmetrical with △ABC on the field grid, and the vertices are all vertices of small squares. Then such a triangle (excluding △ABC itself) has a total of ()
A. 1 B. 2 C. 3 D. 4
2. Consider △ABC symmetrical to the straight line l, △A′B′C′, and the symmetry points of points A, B, and C are respectively A′, B′, and C′. Then the correct one of the following statements is ()
A. AA′ bisects the axis of symmetry perpendicularly
B. The perimeters of △ABC and △A′B′C′ are equal
C. Line segment AB′ is bisected by the axis of symmetry
D. The area of △ABC is bisected by the axis of symmetry
3. As shown in the figure, ∠A=30°, ∠C′=60°, △ABC and △A′B′C′ are symmetrical about the straight line l, then ∠B=__________.
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"Exploring the Nature of Axisymmetry" PPT download of Axisymmetry in Life:
"Exploring the Nature of Axial Symmetry" Download the Axisymmetric PPT in Life Part 1: Teaching Objectives 1. Understand the concepts and meanings of axial symmetry and axisymmetric graphics; 2. Be able to draw the symmetry axis of an axisymmetric graphic, and be able to determine whether a graphic is It is an axis-symmetric figure; 3...
"Exploring the Nature of Axisymmetry" Axisymmetric PPT in Life:
"Exploring the Properties of Axial Symmetry" PPT on Axial Symmetry in Life Part One: Learning Objectives 1. Experience the process of exploring the properties of axial symmetry, accumulate experience in mathematical activities, and develop spatial concepts. 2. Understand the properties of axial symmetry: two axially symmetrical The connection of corresponding points in the graph..
"Exploring the Properties of Axisymmetry" Axisymmetric PPT Courseware 3:
"Exploring the Nature of Axial Symmetry" Axis Symmetry PPT Courseware 3 Preparation for the experimental operation before class: Fold a rectangular paper in half and use the tip of a pen to poke the number 14. Open the paper and lay it flat. Cooperation and communication: 1. In the picture, two 14 what is the relationship? 2. During the process of tying words, click E and...