"Designing with Axial Symmetry" Axisymmetric PPT Courseware in Life

"Designing with Axial Symmetry" Axisymmetric PPT Courseware in Life

Part One: Learning Objectives

1. Be able to complete the given figure into an axially symmetrical figure with a certain straight line as the axis as required. (Key points)

2. Through the paper-cutting process, you can design axially symmetrical graphics based on the axially symmetrical relationship of the graphics. (Difficulty)

Using axial symmetry to design PPT, part 2: collaborative exploration

1. Take a piece of paper 30cm wide and 6cm wide, fold it into sections every 3 centimeters, in reverse and forward, like an "accordion", and draw the letter E on the folded paper. Use a knife to cut the drawn Dig out the letter E and open the "accordion", and you will get a lace with the letter E as the pattern.

(1) In the lace you obtained, what is the relationship between two adjacent patterns? What is the relationship between the two alternate patterns? Tell us your reasons.

Two adjacent patterns form an axially symmetrical figure;

The two alternate patterns are exactly the same size and direction.

(2) If two adjacent patterns are grouped together, what is the relationship between each group of patterns? What about a set of three patterns? Why?

All are axially symmetrical.

(3) In the above activity, if you first fold the paper strip in half lengthwise, then fold it into an "accordion", and then continue the above steps, what kind of lace will you get? Is it an axisymmetric figure? Guess first, then do it.

Get a two-layer lace similar to the one above, which is still an axially symmetrical figure.

2. As shown in the picture: take a thin square paper and fold it in half along the diagonal line to get an isosceles right triangle. Then fold it in half along the high line on the bottom edge and fold the resulting graph paper along the black line in the picture. Cut, remove the 90-degree corner, unfold the folded paper, and lay it flat.

(1) What pattern will you get? Guess first, then do it.

Obtain a figure with two axes of symmetry.

(2) Can you explain why you get such a pattern? Give it a try using what you learned about axial symmetry.

In fact, it is equivalent to folding out the two axes of symmetry of the square.

(3) If you fold the square paper in half three times as shown above (as shown in the picture), then cut it along the arc and remove the smaller part, what will be the result after unfolding? Why?

In fact, it is equivalent to folding out the four axes of symmetry of the square.

(4) When the paper is folded twice, how many axes of symmetry will the cutout have? What about three times?

When the paper is folded twice, the pattern cut out has at least two axes of symmetry;

When the paper is folded three times, the pattern cut out has at least four axes of symmetry.

Using axial symmetry to design PPT, the third part: in-class training

1. Do you know how to cut out the pattern below?

Can you cut out a similar pattern?

2. Can you turn a rectangular paper into a line pattern with just one cut?

Fold it three times along the dotted line and then cut it once.

Using axial symmetry to design PPT, part 4: Class summary

Design patterns using axial symmetry

Obtain an axially symmetrical figure from a plane figure

Design patterns using axial symmetry

Using axial symmetry to design PPT, Part 5: On-site inspection

1. As shown in Figure 1, fold a square piece of paper once diagonally, then dig a round hole in each of the three corners of the resulting triangle, and finally unfold the square piece of paper. The resulting pattern is ( )

2. As shown in the picture, fold the rectangular piece of paper in half to the right along the dotted line AB in the direction of the arrow, then fold it in half along CD, then cut out a small triangle, and then open the piece of paper. The unfolded picture is ( )

3. Fold a square piece of paper in half twice as shown in Figure ① and Figure ②, and then dig out a small triangular hole as shown in Figure ③. The expanded shape will be ( )

4. Use two circles, two line segments, and two triangles to design an axially symmetrical pattern, and explain your design intention and the meaning you want to express.

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