"Basic Properties of Axisymmetry" PPT Courseware 3

Description

"Basic Properties of Axisymmetry" 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 the concept of space.

2. Develop the habit of diligent thinking through hands-on operations, cooperation and communication.

Activity one:

As shown in the figure, after folding a piece of paper, prick a hole with a needle; then unfold the paper, the two pinholes are marked as point A and point A′ respectively, and the crease is marked as l; connect AA′, AA′ and l Intersects at point O.

What did you find (group discussion)?

OA= OA′ AA′⊥ l

A straight line that is perpendicular and bisects a line segment is called the midpoint perpendicular of the line segment.

As shown in the figure, straight line l intersects line segment AB at point O, ∠1=90°, AO=BO, straight line l is the perpendicular bisector of line segment AB.

Activity 2:

Follow the above operation and punch another hole in the folded paper. After unfolding the paper, mark these two pinholes as point B and point B′, connecting AB, A′B′, and BB′. What new discoveries have you made?

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

Activity three:

As shown in the picture, follow the instructions above, punch holes, unfold, mark, and connect wires.

What is the relationship between △ABC and △A′B′C′?

Let’s talk about the properties of axial symmetry

Axisymmetric properties:

1. Two figures that are axially symmetrical are congruent.

2. In two figures that are axially symmetrical, the lines connecting corresponding points are bisected perpendicularly by the axis of symmetry; the corresponding line segments are equal and the corresponding angles are equal.

Example 1 Xiao Ming took a piece of paper, used a small needle to poke "4" on the paper, and then placed the paper in front of the mirror.

(1) Can you draw the position of the straight line l where the mirror is located?

(2) The symmetry points of points A, B, C, and D in the figure are ________ respectively, and the corresponding line segments of line segments AC and AB are ________, CD=________, ∠CAB=________, ∠ACD=________.

(3) Connect AE and BG. Are AE and BG parallel? Why?

Solution: (3) Parallel.

∵A and E, B and G are symmetry points about the straight line l,

∴ l⊥AE , l⊥BG．

∴AE ∥BG.

Class summary

1. Axisymmetric properties:

(1) Two axially symmetric figures are congruent.

(2) In two figures that are axially symmetrical, the lines connecting corresponding points are bisected perpendicularly by the axis of symmetry, the corresponding line segments are equal, and the corresponding angles are equal.

2. In two figures that are axially symmetrical, the lines connecting the symmetry points are parallel to each other or on the same straight line.

3． 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.

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For more information about the "Basic Properties of Axial Symmetry" PPT courseware, please click on the "Basic Properties of Axial Symmetry ppt" tag.

"Basic Properties of Axisymmetry" PPT courseware 2:

"Basic Properties of Axisymmetry" PPT Courseware 2 Review and Consolidation 1: 1. Properties of axial symmetry: (1) In two axially symmetrical figures, the line connecting corresponding points is bisected perpendicularly by the axis of symmetry, (2) Two axially symmetrical figures are congruent. (3) The corresponding line segments are equal, corresponding to...

"Basic Properties of Axisymmetry" PPT courseware:

"Basic Properties of Axial Symmetry" PPT Courseware 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 form axial symmetry. This straight line is the axis of symmetry 1. As shown in the figure:..

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Update Time: 2024-07-06

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 1 industry PPT template

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