UNIT 1 • LESSON 8 ROTATION PATTERNSSetting the StageWHAT YOU WILL LEARNIn this lesson, I will rotate figures in a plane.I can...[list][*]Introduce figures which are built by applying several transformations to one starting figure.[/*][*]Practice rotating line segments around various points.[/*][/list]I will know I learned by...[list][*]Demonstrating that I can describe how to move one part of a figure to another using a rigid transformation.[/*][/list][b] FAMILY MATERIALS:[/b]To review or build a deeper understanding of the math concepts, skills, and practices in this lesson, [url=https://im.openupresources.org/8/teachers/1/family_materials.html]visit the Family Materials provided by Illustrative Mathematics Open-Up Resources. (Links to an external site.)Links to an external site.[/url]8.1: Building a QuadrilateralHere is a right isosceles triangle:[img width=178,height=185]https://hcpss.instructure.com/courses/93828/files/10332691/preview[/img][list=1][*]Rotate triangle ABCABC 90 degrees clockwise around BB. [/*][*]Rotate triangle ABCABC 180 degrees clockwise round BB.[/*][*]Rotate triangle ABCABC 270 degrees clockwise around BB.[/*][*]What would it look like when you rotate the four triangles 90 degrees clockwise around BB? 180 degrees? 270 degrees clockwise?[/*][/list]8.2: Rotating a SegmentCreate a segment ABAB and a point CC that is not on segment ABAB.[url=http://im.openupresources.org/8/students/1/8.html#geogebra-wrapper-YF2EDCTt-1491364065]Geogebra Applet (Links to an external site.)Links to an external site.[/url][list=1][*]Rotate segment ABAB 180∘180∘ around point BB. [/*][*]Rotate segment ABAB 180∘180∘ around point CC. [/*][/list]Construct the midpoint of segment ABAB with the Midpoint tool. [img]https://hcpss.instructure.com/courses/93828/files/10332695/preview[/img][list=1][*]Rotate segment ABAB 180∘180∘ around its midpoint. What is the image of A?[/*][*]What happens when you rotate a segment 180∘180∘?[/*][/list]Are You Ready For More?[img]https://hcpss.instructure.com/courses/93828/files/10332657/preview[/img]Here are two line segments. Is it possible to rotate one line segment to the other? If so, find the center of such a rotation. If not, explain why not.8.3: A Pattern of Four TrianglesHere is a diagram built with three different rigid transformations of triangle ABCABC.Use the applet to answer the questions. It may be helpful to reset the image after each question.[url=http://im.openupresources.org/8/students/1/8.html#geogebra-wrapper-Ccv3FucS-1491364059]Geogebra Applet (Links to an external site.)Links to an external site.[/url][list=1][*]Describe a rigid transformation that takes triangle ABCABC to triangle CDECDE.[/*][*]Describe a rigid transformation that takes triangle ABCABC to triangle EFGEFG.[/*][*]Describe a rigid transformation that takes triangle ABCABC to triangle GHAGHA.[/*][*]Do segments ACAC, CECE, EGEG, and GAGA all have the same length? Explain your reasoning.[/*][/list]SummaryWhen we apply a 180-degree rotation to a line segment, there are several possible outcomes:[list][*]The segment maps to itself (if the center of rotation is the midpoint of the segment).[/*][*]The image of the segment overlaps with the segment and lies on the same line (if the center of rotation is a point on the segment).[/*][*]The image of the segment does not overlap with the segment (if the center of rotation is [i]not[/i] on the segment).[/*][/list]We can also build patterns by rotating a shape. For example, triangle ABC shown here has m(∠A)=60. If we rotate triangle ABC 60 degrees, 120 degrees, 180 degrees, 240 degrees, and 300 degrees clockwise, we can build a hexagon.[img]https://cms-k12oer-staging.s3.amazonaws.com/uploads/pictures/8/8.1.Cycle4.8.png[/img][url=http://creativecommons.org/licenses/by-nc-sa/4.0][img width=87,height=31]https://hcpss.instructure.com/courses/74403/files/8777591/download[/img][/url] [url=http://creativecommons.org/licenses/by-nc-sa/4.0][img]https://du11hjcvx0uqb.cloudfront.net/dist/images/cc/cc_by_nc_sa-01ee261355.png[/img][/url] All Illustrative Mathematics Open Up Resources can be Downloaded for free at [url=http://openupresources.org/]openupresources.org (Links to an external site.)Links to an external site.[/url]. Any additional HCPSS content is offered under a [b][url=http://creativecommons.org/licenses/by-nc-sa/4.0]CC Attribution Non-Commercial Share AlikeLinks to an external site.[/url][/b] license.