In session 5, you witnessed three methods to move figures around: rotation, reflection, and also translation. If you can move whole design in among these ways, and also that design appears unchanged, climate the style is symmetric.

You are watching: When a line of symmetry divides an image

If you have the right to reflect (or flip) a figure over a line and the figure shows up unchanged, climate the figure has reflection symmetry or line symmetry. The line the you reflect over is dubbed the line of symmetry. A line of symmetry divides a figure into 2 mirror-image halves. The dashed lines below are lines of symmetry:

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The dashed lines listed below are not lines the symmetry. Despite they do cut the numbers in half, lock don’t produce mirror-image halves.

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You deserve to use a Mira (image reflector) or simply the procedure of cutting and folding to discover lines of symmetry. Print the PDF version of the figures above, and compare the currently proposed making use of a Mira.

In problems A1 and also A2, lay out the figures or print the PDF papers of the figures and show the currently of symmetry as dashed lines.

Problem A1

For every figure, find all the present of symmetry friend can.

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Problem A2

Find all the present of symmetry for these constant polygons. Generalize a rule about the number of lines of symmetry for consistent polygons.

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The Perpendicular Bisector


If point A’ is the mirror image of suggest A in a number with a line of symmetry, then the heat of the contrary is the perpendicular bisector of the segment AA’.

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You deserve to use that fact to reflect figures over lines without making use of a maker like a Mira. Mean you want to reflect the triangle listed below over the line shown. Come reflect point A, attract a segment from A perpendicular to the line. Proceed the segment past the line till you’ve doubled its length. You currently have point A’, the mirror picture of A.

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Repeat the procedure for the various other two endpoints, and connect castle to form the triangle.

Problem A3

For each figure, reflect the number over the line presented using perpendicular bisectors. Check your job-related with a Mira.

Printable PDF of figures

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Video Segment

In this video segment, the participants explain different ways in i beg your pardon they come up with perpendicular bisectors to reflect the numbers over the line of symmetry.

Did you use the same an approach as displayed in the video clip segment? Did you come up with a different method of solving the problems?

You can discover this segment top top the session video clip approximately 11 minutes and also 9 seconds after the Annenberg Media logo.

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Solutions


Problem A1

The isosceles trapezoid has actually one line of symmetry, the perpendicular bisector of the base. The scalene triangle has no currently of symmetry. The isosceles triangle has actually one line of symmetry, the perpendicular bisector that the base. The ellipse has actually two currently of symmetry, one along the significant and one follow me the minor axis. The rectangle has actually two currently of symmetry, the perpendicular bisector the the longer sides, and the perpendicular bisector of the much shorter sides. The circle has actually infinitely plenty of lines that symmetry, any kind of line going with the center. (Any diameter is a heat of symmetry.) The parallelogram pictured has no currently of symmetry. No does the trapezoid.