SymmetryEssentlal'questlore How do you determine whetherafigure has line symmetryor rotational symmetry?

A figure has symmetrY. if there is a rigid motion such that the imageofthe figure coincides-with the pre-image.

Afigure haslihesfin,tnet~y (orteflection symmetry) «..if the figure can be reflected across a line so thatthe ~- - - - ..- -•.•....•..-.-.-- _~~;yir;::::try.image coincideswiththe pre-image. Inthis case, theline of reflection is called the u;neofs,~eirY.

Determine whether each figure has line symmetry. If so, draw all lines of symmetry.(Use the steps given for figure A to help you with the other figures.)

it. Rectangle

••.Trace the figure on a piece of tracing paper.

@ Checkto see if the figure can be folded along a straight line so thatone half of the figure coincides with the other half. If so, the figurehas line symmetry and the crease represents the line of symmetry.

$ The rectangle has line symmetry. The two lines of symmetryare shown.

Isosceles trapezoid Parallelogram Regular hexagon

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What can you say about a triangle that has exactly one line of symmetry?\'\Ihy?

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1b. Does every non-straight angle have a line of symmetry? Explain.

Unit4 107 Lesson 1

AJigure has!~o!ationalisYmpiettiif the figure can be rotated about apoint by an angle greater than 0° and less than or equal to 180° so thatthe image coincides with the pre-image. The smallest angle that mapsthe tlgureonto .itselfis theang!e(")fftl,tlltio~a.l~~etfy. df;.....•.....•.........~.!! ' ·A.n9

1eOf. rotational. \ symmetry: 90°. . \

Determine whether each figure has rotational symmetry. If so, give the angle of rotationalsymmetry. (Use the steps given for figure A to help you with the other figures.)

Rectangle

" Trace the figure on a piece of tracing paper.

"Without moving the tracing paper, firmly place the point of yourpencil onthecenterpoint of the figure. Rotate the tracing paper.Check to see if the figure coincides with itself after a rotation by anangle less than or equal to 180°.

e The rectangle has rotational. symmetry. The angle of rotationalsymmetry isl80°.

Isosceles trapezoid Parallelogram

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•

Regular hexagon

Is it possible for a figure to have rotational symmetry but not have line symmetry?Explain.

student claims that a figure has rotational symmetry and .thattheangle of rotational symmetry is 360°. Critique the student's statement.

Unit 4 108 Lesson..l