"Exploring the Properties of Axisymmetry" Axisymmetric PPT Courseware

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"Exploring the Properties of Axisymmetry" Axisymmetric PPT Courseware

Review introduction

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 this figure.

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.

Use your hands and brain to explore new knowledge:

1. Move your hands:

(1) Fold a rectangular white paper in half, draw a line segment AB at will, use the tip of the pen to poke holes at points A and B, and then unfold the paper and flatten it.

(2) In the two pierced holes on the other side of the crease, the pierced hole made by point A is represented by point A`, and the pierced hole made by point B is represented by point B`, and the two points A` and B` are connected. , get line segment A` B`, and then connect point A, point A` and point B, point B` respectively to get line segment AA` and line segment B B`

(3) Draw the straight line where the crease is located and indicate it with the letter m.

2. Use your brain:

(1) What is the relationship between points A and A` with respect to the crease m? What about points B and B`? Please explain why.

In an axially symmetric figure, after folding in half along the axis of symmetry, two points that can overlap each other are called corresponding points about the axis of symmetry.

(2) What is the positional relationship between the line segment A A` connecting the corresponding points A and A` and the axis of symmetry m? What about line segment BB`? Can you explain why? Collaborate and communicate with peers.

(3) Can you tell the relationship between the line segments connected to the corresponding points and the axis of symmetry?

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

(4) What is the relationship between line segments AB and A`B` with respect to straight line m? Please explain why.

In an axially symmetrical figure, after folding in half along the axis of symmetry, two line segments that can overlap each other are called corresponding line segments about the axis of symmetry.

(5) Can you tell the size relationship between corresponding line segments?

Conclusion ②: The corresponding line segments are equal

Quick answer:

In the figure below, �ABC and �A`B`C` are axially symmetrical about the straight line m.

(1) What are the corresponding points of points A, B, and C on the straight line m?

(2) What is the relationship between the line segments A A`, B B`, C C` and the axis of symmetry m? Why?

(3) Who are the corresponding line segments of line segments AB, BC, and AC with respect to straight line m? What is the size relationship between them? Why?

Use your brain:

In the figure below, �ABC and �A`B`C` are axially symmetrical about the straight line m

If �ABC is folded in half along the axis of symmetry m, which angle coincides with ∠A? What is their relationship with respect to straight line m?

In an axially symmetric figure, after folding in half along the axis of symmetry, the two angles that can overlap each other are called the two angles corresponding to each other about the axis of symmetry.

Do you know the size relationship between corresponding angles?

Conclusion ③: Corresponding angles are equal

Do it:

The picture on the right is an axisymmetric figure:

(1) Can you 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?

Based on the above questions, what conclusion can you draw?

The nature 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.

consolidate new knowledge

1. If two figures are symmetrical about a straight line, then the line segments connecting corresponding points are bisected perpendicularly by the axis of symmetry.

2. The figure below is an axially symmetrical figure. The equal line segments are AB=CD, BE=CE, and the equal angles ∠B=∠C.

3． Two figures are symmetrical about a certain straight line, and the symmetry point must be ( )

A. On both sides of this straight line B. On the same side of this straight line

C. On this straight line D. On both sides of this straight line or on this straight line.

4. After an axially symmetrical figure is folded in half along the axis of symmetry, the parts on both sides of the axis of symmetry ( )

A. Completely coincident B. Not completely coincident

C. Both

Summary of the lesson

What properties of axial symmetry have you mastered through studying this class?

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.

Homework

1. Complete Exercise 5.2 Knowledge and Skills independently: Questions 1 and 2; Problem Solve Questions 1 and 2.

2. Group cooperation to explore and expand contacts: Question 1.

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Update Time: 2024-09-05

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