"Exploring the Properties of Axisymmetry" Axisymmetric PPT Courseware 3

Description

"Exploring the Properties of Axisymmetry" Axisymmetric PPT Courseware 3

Preparation before class

Experimental operation: 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.

Cooperation and exchange:

1. What is the relationship between the two "14" in the picture?

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 connecting point E and point E/ and l? Point F What about point F/?

3. What is the relationship between line segments AB and A/B/? What about CD and C/D/?

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

In the figure, after folding in half along the symmetry axis, point A coincides with A/, and the corresponding point of point A about the symmetry axis is point A/. Similarly, the corresponding line segment of line segment AB about the symmetry axis is line segment A/B/, ∠ The corresponding angle of 1 about the axis of symmetry is ∠2.

Situation introduction

Observe this axisymmetric figure:

1. Find its axis of symmetry;

2. What is the relationship between the line segment connecting point A and point A/ and the axis of symmetry? What about the line segment connecting point B and point B/?

3. What is the relationship between line segment AD and line segment A/D/? What about line segment BC and line segment B/C/?

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

Properties of axial symmetry:

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.

Do it

The figure shows half of a pattern, and the dotted line is the axis of symmetry of the pattern.

1. Can you guess the shape of the whole pattern?

2. Can you draw the other half of this pattern?

Consolidate and improve

1. As shown in Figure �ABC and �A/B/C/ are symmetrical about the straight line l, A/B/=6cm, ∠ABC=90°, then ∠A/B/C/ =____°, AB=___cm.

2. Which of the following statements is correct ( )

A. The line segments connected to the corresponding points of an axially symmetric figure bisect the axis of symmetry perpendicularly;

B. If there is a point on an axis-symmetric figure on the axis of symmetry, then the point coincides with its corresponding point;

C. The corresponding points of an axially symmetrical figure must be on both sides of the symmetry axis;

D. Two congruent figures must be axially symmetrical.

3. As shown in the figure, �ABC and �A/B/C/ are symmetrical about the straight line l. Are these two triangles congruent? If �ABC≌�A/B/C/, then �ABC and �A/B/C /Is it necessarily symmetrical about the straight line l?

Explore patterns

�ABC and �A/B/C/ are symmetrical about the straight line l, and extend the corresponding line segments AB and A/B/. Do the two extended lines intersect? What is the relationship between the intersection point and the axis of symmetry l? What about extending other corresponding line segments? Find a few more axially symmetrical figures and observe them. What patterns can you find?

Rule: If two figures are symmetrical about a straight line, then any pair of corresponding line segments or their extensions on the two figures intersect at one point, and the intersection point is on the axis of symmetry.

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Update Time: 2024-09-28

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