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Objective

Common Core State Standards

■ 4.G.3

4Geometry

Line SymmetryIdentifying lines of symmetry in polygons helps students recognize symmetry in the world around them. Line symmetry is the basis of reflection, one of the transformations used in geometric thinking. The concept of line symmetry complements the concepts of congruence and similarity.

Talk About ItDiscuss the Try It! activity.

■ Ask: Are all lines that divide a shape in half called lines of symmetry?

■ Ask: Why is a line of symmetry sometimes called a mirror line or a line of reflection?

■ Ask: How many lines of symmetry does the hexagon have?

■ Say: Three of the lines of symmetry divide the hexagon into trapezoids. Ask: What shapes is the hexagon divided into by the other lines of symmetry? Students should see that the shapes are irregular pentagons.

Solve ItReread the problem with students. Have them write a paragraph to explain what they know about line symmetry and how they used the mirror to find lines of symmetry.

More IdeasFor other ways to teach line symmetry—

■ Have students use Pattern Blocks and a GeoReflector™ Mirror to construct more shapes using the same method they used to construct the hexagon in Step 2 of the Try It! activity. Have them draw the shapes that they create.

■ Have students create figures with line symmetry using AngLegs®. Students can make two halves separately and snap the halves together to make a symmetrical shape.

Formative AssessmentHave students try the following problem.

Which figure has three lines of symmetry?

A . B . C . D .

Geometry

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Materials• Pattern Blocks (1 hexagon and

7 trapezoids per group)• GeoReflector™ Mirror (1 per group)• paper (1 sheet per group)• pencils (1 per group)

Try It! 30 minutes | Groups of 4

Here is a problem about line symmetry.

Kim’s company makes Pattern Blocks. They make trapezoid blocks by cutting

hexagon blocks in half. How many ways can a hexagon block be cut in half to

make a pair of trapezoid blocks? Consider other lines that divide the hexagon

into halves. In all, how many different lines produce halves that are mirror

images of each other?

Introduce the problem. Then have students do the activity to solve the problem. Distribute Pattern Blocks, GeoReflector Mirrors, paper, and pencils to students.

1. Have students use a hexagon block to trace three hexagons onto a sheet of paper, all oriented the same way. Say: Use trapezoid blocks to fill in the hexagons. Show the different ways a hexagon can be cut in half. Guide students to orient the “cut” lines three different ways.

3. Say: Trace another hexagon onto your sheet of paper. Use the mirror to find and draw all the lines of symmetry of the shape.

2. Have students select another trapezoid block and use it with the GeoReflector Mirror to “construct” a regular hexagon. Say: Half of the hexagon is formed by the trapezoid block and the other half is formed by the image in the mirror. Introduce the concepts of symmetry, line of symmetry, and mirror image.

Students might think that a line of symmetry is any line that divides a shape into two equal halves. Reiterate that the halves must be mirror images of each other in order for the dividing line to be classified as a line of symmetry. Have students investigate this idea with a simple shape, such as a rectangle, and a GeoReflector Mirror.

Name GeometryLesson

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Hands-On Standards, Common Core Edition

4

Use Pattern Blocks to model an equilateral triangle. Trace the triangle on paper. Use the GeoReflector Mirror to find all lines of symmetry. How many lines of symmetry are there?

1.

__________________________

Using Pattern Blocks and the GeoReflector Mirror, model all lines of symmetry of a square. One line of symmetry is shown in the GeoReflector. Sketch the model and draw the lines of symmetry. How many lines of symmetry are there?

2.

__________________________

How many lines of symmetry does each shape have?

3.

____________________________

4.

____________________________

Answer Key

Download student pages at hand2mind.com/hosstudent.

(Check students’ work.)

(Check students’ work.)

3

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Hands-On Standards, Common Core Edition

Challenge! Can a shape have both a horizontal line of symmetry and a vertical line of symmetry? Draw an example. Can a shape have a horizontal line of symmetry and not have a vertical line of symmetry? Draw an example.

Answer Key

Download student pages at hand2mind.com/hosstudent.

Challenge: (Sample) Yes; a square has both lines of symmetry; yes; a trapezoid can have only one line of symmetry, either vertical or horizontal.

Name GeometryLesson

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Hands-On Standards, Common Core Edition www.hand2mind.com

4

Use Pattern Blocks to model an equilateral triangle. Trace the triangle on paper. Use the GeoReflector Mirror to find all lines of symmetry. How many lines of symmetry are there?

1.

__________________________

Using Pattern Blocks and the GeoReflector Mirror, model all lines of symmetry of a square. One line of symmetry is shown in the GeoReflector. Sketch the model and draw the lines of symmetry. How many lines of symmetry are there?

2.

__________________________

How many lines of symmetry does each shape have?

3.

____________________________

4.

____________________________

143

Name

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TA hand

2mind

™

Hands-On Standards, Common Core Editionwww.hand2mind.com

Challenge! Can a shape have both a horizontal line of symmetry and a vertical line of symmetry? Draw an example. Can a shape have a horizontal line of symmetry and not have a vertical line of symmetry? Draw an example.