"Exploring the Nature of Axial Symmetry" Axisymmetric PPT Download in Life

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"Exploring the Nature of Axial Symmetry" Axisymmetric PPT Download in Life

Part One: Teaching Objectives

1. Understand the concepts and meanings of axial symmetry and axisymmetric graphics;

2. Be able to draw the symmetry axis of an axially symmetrical figure, and be able to judge whether a figure is an axially symmetrical figure;

3. Understand and master the basic properties of axial symmetry;

4. Know how to draw axially symmetrical figures and be able to draw axially symmetrical figures of known figures.

Exploring the properties of axial symmetry PPT, part 2: introduction of new lesson

Review old knowledge

1. 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 __________, and this straight line is called the __________ of the figure.

2. For two figures, fold one figure in half along a certain straight line. If it can completely coincide with the other figure, then it is said to be ____________________, and this straight line is __________.

Exploring the properties of axial symmetry PPT, part three: exploration of new knowledge

1. Properties of axial symmetry

Example 1 As shown in the figure, △ABC and △A′B′C′ are symmetrical about the straight line MN. Points A′, B′, and C′ are the symmetry points of points A, B, and C respectively. Line segments AA′, BB′, and CC′ What does it have to do with straight line MN?

The properties of axial symmetry of graphics

If two figures are symmetrical about a straight line, then the axis of symmetry bisects the line segment connecting any pair of corresponding points perpendicularly.

Example 2 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 the "14" on both sides of the crease in the picture?

The "14" on both sides of the crease is symmetrical about the crease.

(2) During the process of tying, point E coincides with point E', and point F coincides with point F'. Let the straight line where the crease is located be l, what is the relationship between the line segment EE' connecting point E and point E' and the straight line l? Relationship? What about the line segment connecting point F and point F'?

Both line segment EE' and line segment FF' can be bisected perpendicularly by straight line l.

(3) What is the relationship between line segment AB and line segment A'B'? What about line segment CD and line segment C'D'?

Line segment AB=line segment A'B', line segment CD=line segment C'D'.

(4) What is the relationship between ∠1 and ∠2? What about ∠3 and ∠4? Tell me your reasons.

∠1=∠2,∠3=∠4.

Properties of axially symmetrical figures

In an axially symmetrical figure or two axially symmetrical figures, the line segments connecting corresponding points are bisected perpendicularly by the axis of symmetry.

As shown in the figure, MN is the symmetry axis of the pentagon in the figure,

It can be obtained that line segment AA’ is bisected perpendicularly by the axis of symmetry MN, that is, OA=OA’,AA’⊥MN.

In conclusion

In an axially symmetrical figure or two axially symmetrical figures:

1. The line segments connected to corresponding points are bisected perpendicularly by the axis of symmetry;

2. The corresponding line segments are equal;

3.Corresponding angles are equal.

2. Make axially symmetrical figures

Interactive exploration

Question 1: How to draw an axis-symmetric figure of a point?

Draw the symmetry point P′ of point P with respect to the straight line l.

practice:

(1) Draw a vertical line l passing through point P, and the vertical foot is point O;

(2) Intercept OP′=OP on the vertical line, point P′ is the symmetry point of point P with respect to the straight line l.

Question 2: How to draw a symmetrical figure of a line segment?

Given line segment AB, draw the symmetrical line segment of line segment AB about straight line l.

Exploring the properties of axial symmetry PPT, Part 4 content: Class summary

Axisymmetric properties

1. The line segment connected to the corresponding point is bisected perpendicularly by the axis of symmetry,

2. The corresponding line segments are equal,

3.Corresponding angles are equal

Draw an axially symmetrical figure

Drawing principles

The line segment connecting the corresponding points bisects the axis of symmetry perpendicularly

Drawing method

1. Find feature points;

2. Make a vertical line;

3. Cut to equal length;

4. Connect in sequence

Exploring the properties of axial symmetry PPT, Part 5: Classroom quiz

1. The first step to find the symmetry point of a known point about a straight line is ()

A. Draw a straight line through a known point and intersect the known straight line

B． Draw a straight line through a known point perpendicular to the known straight line

C． Draw a straight line through a known point parallel to the known straight line

D． uncertain

2. As shown in the figure, complete the following figures into symmetrical figures about the straight line l.

3. As shown in the figure, △ABC and △DEF are symmetrical about the straight line MN, then the following conclusion is wrong ()

A. AB∥DF

B． ∠B=∠E

C． AB=DE

D． The line connecting AD is bisected perpendicularly by straight line MN.

4. As shown in the figure, in Rt△ABC, ∠ACB=90°, ∠A=50°, fold it so that point A falls at point A′ on side CB, and the fold is CD, then ∠A′DB The degree of is _______.

5. As shown in the figure, half of a pattern is shown. The dotted line l is the axis of symmetry of the pattern. What is the shape of the entire pattern? Please draw its other half accurately.

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For more information about the PPT courseware "Axisymmetry in Life Exploring the Nature of Axial Symmetry", please click the Axial Symmetry in Life PPT Exploring the Nature of Axial Symmetry PPT tag.

"Exploring the Nature of Axisymmetry" Axisymmetric PPT teaching courseware in life:

"Exploring the Nature of Axial Symmetry" The first part of the Axisymmetric PPT teaching courseware in life: Learning objectives 1. Explore and master the properties of axial symmetry. (Key points) 2. Be able to use the properties of axial symmetry to make symmetrical points, symmetrical figures, and symmetry Axis, etc. (difficulty) ... ...

"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...

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Update Time: 2024-07-11

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