"Perpendicular Bisector of Line Segment" Proof PPT Courseware 2

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"Perpendicular Bisector of Line Segment" Proof PPT Courseware 2

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.

Method: 1. Take points A and B as the center points of the circles and draw arcs with a length greater than AB/2 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.

Theorem: A point on the perpendicular bisector of a line segment is equidistant from both endpoints of the line segment.

As shown in the figure,

∵AC=BC,MN⊥AB,P is any point on MN (known),

∴PA=PB (the distance between the point on the perpendicular bisector of the line segment and the two endpoints of the line segment is equal).

Cut a triangular piece of paper and fold it to find the perpendicular bisector of each side.

Observe these three perpendicular bisectors, what do you find?

Conclusion: The perpendicular bisectors of the three sides of a triangle intersect at one point.

Do you want to prove this proposition? Can you prove this proposition?

Discuss

Given one side of a triangle and the height of this side, can you make a triangle?

If so, how many can be made? Are all the triangles congruent?

Given the base and height of the base of an isosceles triangle, can you use a ruler and compass to make an isosceles triangle? How many can you make?

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Update Time: 2024-11-18

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