"Symmetry of Circles" PPT courseware 2

Description

"Symmetry of Circles" PPT courseware 2

learning target:

Understand the axial symmetry of a circle and its related properties;

Understand the vertical diameter theorem;

Be able to use the vertical diameter theorem to solve related problems.

main difficulty:

Perpendicular diameter theorem and its applications.

Communication and presentation of preview plans:

Knowledge preparation:

What is an axisymmetric figure? What axisymmetric shapes have we learned?

If a figure is folded in half along a straight line and the parts on both sides of the straight line overlap each other, then the figure is called an axially symmetrical figure.

Such as line segments, angles, isosceles triangles, rectangles, rhombuses, isosceles trapezoids, squares, etc.

Concepts related to circles

The part between any two points on a circle is called an arc, or arc for short.

An arc with two points A and B as endpoints is recorded as AB and pronounced as "arc AB".

An arc smaller than a semicircle is called a minor arc, such as AB (using two letters).

An arc that is larger than a semicircle is called a superior arc, such as ADB (with three letters).

The line segment connecting any two points on the circle is called a chord (such as chord AB).

The chord passing through the center of the circle is called the diameter (such as diameter AC).

Self-learning:

1. Is a circle an axially symmetrical figure?

A circle is an axially symmetrical figure.

If so, what is its axis of symmetry? How many axes of symmetry can you find?

The axis of symmetry of a circle is any straight line passing through the center of the circle. It has countless axes of symmetry.

How did you find the axis of symmetry?

The above problems can be solved by using the folding method.

2. Follow the steps below:

1) Take out a circular piece of paper and fold the circle in half.

Make the two halves of the circle coincide.

2) Get a creased CD.

3) Pick any point A on ⊙O, and draw the vertical line of the CD fold through point A to obtain a new fold. Among them, point M is the intersection of the two folds, that is, the vertical foot.

4) Open the paper and make the new fold intersect the circle at another point B, as shown in the picture above.

During the above operation, what equal line segments and equal arcs did you discover?

Why are they equal?

Study 1: Three languages ​​of the vertical diameter theorem

Theorem A diameter perpendicular to a chord bisects the chord and the two arcs subtended by the chord.

∵ CD is the diameter,

CD⊥AB,

∴ AM=BM,

AC=BC, AD=BD.

Condition Conclusion

①One diameter ③The diameter bisects the chord

②Perpendicular to the chord ④The minor arc that bisects the chord

⑤The superior arc subtended by the bisector chord

Exploration 2: Application of the Perpendicular Diameter Theorem

Example 1: As shown in the figure, ⊙O with the vertex O of △OAB as the center of the circle intersects AB at points C and D, and AC=BD.

Verify: OA=OB.

Example 2: As shown in the figure, it is known that in ⊙O, the length of chord AB is 8 cm, and the distance from the center O to AB is 3 cm. Find the radius of ⊙O.

Compliance in class:

1. In ⊙O, if CD⊥AB is in M ​​and AB is the diameter, then which of the following conclusions is incorrect ( )

A. AC=AD B. BC=BD

C. AM=OM D. CM=DM

2. It is known that the diameter of ⊙O is AB=10, the chord CD is ⊥AB, the vertical foot is M, and OM=3, then CD=_____.

3. In ⊙O, CD ⊥AB is in M, and AB is the diameter. If CD=10, AM=1, then the radius of ⊙O is _____.

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For more information about the "Symmetry of Circles" PPT courseware, please click the Symmetry of Circles ppt tag.

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Update Time: 2024-10-05

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

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