"Perpendicular bisectors of line segments" PPT courseware 7

Description

"Perpendicular bisectors of line segments" PPT courseware 7

question:

1. Is the line segment an axially symmetrical figure? If it is the axis of symmetry, what is it?

2.What is the perpendicular bisector of a line segment?

3. How to make the perpendicular bisector of a line segment?

Thinking: Is there any other way to determine the perpendicular bisector of a line segment?

Rule and compass drawing method:

practice:

1. Take points A and B as the center points of the circles, which are larger than 1/2AB

The length is the radius, and the arc is drawn to intersect at points E and F;

2. Draw a straight line through points E and F.

question

1. How many isosceles triangles can be made with the known line segment AB as the base?

2. If you don’t use a ruler and compass but use a set square, can you draw the isosceles triangle required above?

3. If you only use a ruler, can you draw the isosceles triangle required above?

perpendicular bisector of line segment

Hands-on operation: Draw the mid-perpendicular line MN of line segment AB, and the vertical foot is C;

Take any point P on MN and connect PA and PB;

Measure it: What can you find about the length of PA and PB?

What rules can you draw from this?

Proposition: The distance between a point on the perpendicular bisector of a line segment and the two endpoints of the line segment is equal.

Property theorem: The distance between a point on the perpendicular bisector of a line segment and the two endpoints of the line segment is equal.

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

1. Property theorem: The distance between a point on the perpendicular bisector of a line segment and the two endpoints of the line segment is equal.

2. The converse theorem: A point equidistant from the two endpoints of a line segment is on the perpendicular bisector of the line segment.

3. The set definition of perpendicular bisectors of line segments:

The perpendicular bisector of a line segment can be thought of as the set of all points that are equidistant from the two endpoints of the line segment.

practise

1. As shown in the figure, DE is the perpendicular bisector of line segment AB. The following conclusion must be true ( )

A． ED=CD

B． ∠DAC = ∠B

C. ∠C>2∠B

D. ∠B +∠ADE=90°

2. As shown in the figure, in △ABC, the perpendicular line BC intersects the hypotenuse AB at D. The equal line segments in the figure are ( )

A. Group 1

B. Group 2

C. 3 groups

D. Group 4

3. It is known that as shown in the figure, the y-axis bisects line segment BC perpendicularly, point A is on the y-axis, and points B and C are on the x-axis.

(1) If the coordinates of point C are (3, 0), then the coordinates of point B are _______;

(2) If the coordinates of point B are (m, 0), then the coordinates of point C are ________.

4. As shown in the figure, DE is the perpendicular bisector of side AB of △ABC, D is the vertical foot, DE intersects AC at point E, and AC=8, BC=5, then the perimeter of △BEC is _______.

summary

a method

A new way to prove that line segments are equal: use the property of perpendicular bisectors of line segments.

two theorems

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

Points equidistant from both ends of a line segment lie on the perpendicular bisector of the line segment.

Three kinds of drawing

origami;

Draw a vertical line through the midpoint;

Rule and compass drawing method

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"Perpendicular bisectors of line segments" PPT courseware 9:

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"Perpendicular bisectors of line segments" PPT courseware 8:

"Perpendicular Bisectors of Line Segments" PPT Courseware 8 Teaching Objectives 1. Be able to tell the theorem and converse theorem of perpendicular bisectors of line segments, and be able to use these two theorems differently. 2. Understand the application of mathematics learning methods, observation, generalization, verification, comparison, etc. in this lesson. 3..

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Update Time: 2024-11-17

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

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