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Course: High school geometry>Unit 2

Lesson 4: Symmetry

Intro to rotational symmetry

Sal checks whether various figure are symmetrical under a 180 degrees rotation. Created by Sal Khan.

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• can a shape have line symmetry and not rotational?
• yes, there are several shapes which don't have rotational symmetry, but have a line of symmetry.
e.g- an isosceles trapezium, semi circle etc.
hope this helped
• Hey sal, you say that the parallelogram is the same shape but even if it is its flipped upside down. Does that count at the same? or does it make it different.
• If you were taking the markings on the parallelogram in consideration, they would be flipped, so it would not be the same. Otherwise, the shape itself would look exactly the same.
• From other geometry videos and lessons we have learned about similarity and congruency in polygons, particularly triangles. In these lessons we intuitively learned that the position of the polygons did not matter when it comes to proving similarity and congruency. I.e. if two triangles are rotated 90 degrees from each other but have 2 sides and the corresponding included angles formed by those sides of equal measure, then the 2 triangles are congruent (SAS). Further, regardless of how we re-position those triangles, they remain congruent. Now comes Transformations that teach us that simply re-positioning the same polygon makes it 'different' or 'changed' somehow from the original. Does anyone else find this confusing?
• Dilations are the only "change" in any figure. They either increase or reduce the size of the figure. All other transformations only change how the figure is positioned. Sal considers rotations of a figure as a change, and it can be legitimately considered that way, but for you, think of it as, say, congruent triangles positioned differently (they are still congruent!)
• Hasn't Sal been saying rotating by a positive number is counter-clockwise? but he is rotating clockwise in this video.
I don't understand.
• You are correct in that Sal is rotating in the negative angle direction. One note is that rotating 180 degrees ends up the same no matter which way you rotate. I guess he is doing absolute value for the purpose of the video.
• I know a circle has ∞ lines of symmetry, but does it have 0. 0𝄇 1 (point 0 repeating 1) degrees of rotational symmetry? Or is the previous number equal to zero? Explain please.
http://en.wikipedia.org/wiki/Infinitesimal
• khan has really helped me with 8th grade thank mmkers
• Hasn't Sal been saying rotating by a positive number is counter-clockwise? but he is rotating clockwise in this video.
• rotating 180° or -180° gets to the same point not like 90° and -90° (270°)
• What does rotational mean?
• Rotation is when one turns something by a certain angle/ degree.