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Authoritative PPT Summary
"Axisymmetric" PPT courseware 6
If a figure is folded along a straight line and the parts on both sides of the straight line overlap each other, then the figure is called an axially symmetric figure, and the straight line is called the axis of symmetry.
practice
The figures below are all axisymmetric figures. Please find the axis of symmetry of each figure respectively.
think about it
Look at each set of patterns in the picture below. What do you find?
If two figures are folded in half along a straight line so that they completely overlap, then the two figures are axially symmetrical, and this straight line is the axis of symmetry.
Discuss
Are axisymmetric graphics and axial symmetry the same thing? Are they different?
difference:
Axisymmetric graphics for a graphic.
Axial symmetry is for two figures.
think
As shown in the figure, △ABC and △A'B'C' are symmetrical about the straight line MN. Points A, B, and C are the symmetry points of points A', B', and C' respectively. Line segments AA', BB', CC' and MN what is the relationship?
Points A and A′ are symmetry points. Suppose AA′ intersects the symmetry axis MN at point P. After folding △ABC and △A′B′C′ along the straight line MN, points A and A′ coincide, so we have:
ＡＰ＝ＰＡ′，∠ＭＰＡ＝ ∠ＭＰＡ′＝９0°
The line where the axis of symmetry lies passes through the midpoint of the line segment connected to the symmetry point and is perpendicular to this line segment.
Definition: A straight line that passes through the midpoint of a line segment and is perpendicular to the line segment is called the perpendicular bisector of the line segment, also called the perpendicular.
Geometry language:
∵MN is the perpendicular bisector of AA′
∴AP=PA′, ∠MPA= ∠MPA′=90°
Axisymmetric properties:
If two figures are axially symmetrical about a certain straight line, then the two figures are congruent, their corresponding line segments are equal, their corresponding angles are equal, and the line segments connected to the corresponding points are bisected perpendicularly by the axis of symmetry.
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"Axisymmetric" PPT:
"Axisymmetric" PPT Part 1 Content: New Lesson Introduction What characteristics did you find of these buildings? There are many symmetrical things and phenomena in life. Boats, people, plants and reflections in the water are all symmetrical. Take a small mirror and place it on an axially symmetrical figure or object...
"Axisymmetric" PPT courseware 5:
"Axisymmetric" PPT courseware 5 Review of old knowledge What is an axially symmetric figure? What is the axis of symmetry? If a figure is folded along a straight line and the parts on both sides of the straight line can completely overlap, the figure is called an axially symmetric figure. This straight line is called the axis of symmetry.
"Axisymmetric" PPT courseware 4:
"Axisymmetric" PPT courseware 4 We say that two such figures form _____. This straight line is called _____. The symmetrical points in the two figures (that is, the points that overlap each other in the two figures after folding in half) are called _____. If two The graph is axially symmetrical about a certain straight line, then...