"Perpendicular bisectors of line segments" PPT courseware 2

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"Perpendicular bisectors of line segments" PPT courseware 2

learning target

1. Experience the formation process of the concept of the perpendicular bisector of a line segment, understand the axial symmetry of the line segment, further experience the characteristics of axial symmetry, and develop the concept of space.

2. Be able to use a ruler and compass to draw the perpendicular bisector of a known line segment.

3. Use drawing and experiment methods to explore the property theorems and inverse theorems of vertical bisectors of line segments.

Experimentation and research:

Test: Use the following method to observe whether the line segment is an axially symmetrical figure?

Ask the students to draw the line segment AB and its midpoint M in the exercise book, and then draw the perpendicular line CD of AB through the point M. Fold the paper in half along the straight line CD and observe whether the line segments MA and MB completely overlap?

Conclusion: Line segments MA and MB completely coincide, therefore, line segment AB is an axially symmetrical figure.

Question 1: Since line segment AB is an axially symmetrical figure. So what is its axis of symmetry?

Question 2: What characteristics or characteristics does linear CD have?

Definition: A straight line that is perpendicular and bisects a line segment is called the perpendicular bisector of the line segment. Also called the center vertical line.

As shown in the figure above, straight line CD is the perpendicular bisector of line segment AB.

Note: ①The mid-perpendicular of the line segment is a straight line. ② There is no perpendicular line between straight lines and rays.

perpendicular bisector of line segment

Hands-on operation: draw the mid-perpendicular line CD of line segment AB, with the vertical foot M; pick any point E on CD to connect EA and EB; measure: the lengths of EA and EB. What can you find?

What rules can you draw from this?

Proposition: The distance from a point on the perpendicular bisector of a line segment to both endpoints of the line segment is equal.

Properties of perpendicular bisectors of line segments:

Points on the perpendicular bisector of a line segment are equidistant from both endpoints of the line segment.

Converse theorem of properties of perpendicular bisectors of line segments

Converse Theorem: A point equidistant from the two endpoints of a line segment lies on the perpendicular bisector of the line segment.

As shown in the figure,

∵EA=EB(known),

∴Point E is on the perpendicular bisector of AB (a point equidistant from the two endpoints of a line segment is on the perpendicular bisector of the line segment).

How to create perpendicular bisectors of line segments

Use a ruler and compass to draw the perpendicular bisector of the line segment.

Known: line segment AB, as shown in the figure.

Find: the perpendicular bisector of line segment AB.

practice:

1. Take points A and B as the center of the circle and draw an arc with a length greater than 1/2 AB as the radius. The two arcs intersect at points C and D.

2. Make a straight line CD.

Then straight line CD is the perpendicular bisector of line segment AB.

Please explain why CD is the perpendicular bisector of AB, and communicate with your peers.

practise

1. As shown in the figure, it is known that straight line MN is the perpendicular bisector of line segment AB, the vertical foot is D, and point P is a point on MN. If AB=10 cm, then BD=______cm; if PA=10 cm, then PB=________cm ;At this time, PD=_______cm.

2. As shown in the figure, in △ABC, the perpendicular bisectors of AC intersect AC at E and BC at D. The perimeter of △ABD is 12 cm, AC=5cm, then AB+BD+AD=_____cm; AB+BD +DC=______cm; The perimeter of △ABC is ______cm

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Update Time: 2024-10-02

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

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