Below are photos of 4 quadrilaterals: a square, a rectangle, a trapezoid and a parallelogram.

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For every quadrilateral, find and draw every lines of symmetry.

You are watching: Quadrilateral with two lines of symmetry


IM Commentary

This task provides students a possibility to experiment through reflections the the plane and their influence on specific varieties of quadrilaterals. That is bothinteresting and important that these varieties of quadrilaterals have the right to be differentiated by their lines the symmetry. The only pictures lacking here, indigenous this suggest of view, room those that a rhombus and a basic quadrilateral i m sorry does no fit into any of the distinct categories thought about here.

This job is ideal suited because that instruction back it could be adjusted for assessment. If students have not however learned the terminology because that trapezoids and also parallelograms, the teacher can start by explaining the an interpretation of those terms. 4.G.2 claims that students need to classify figures based on the existence or absence of parallel and also perpendicular lines, therefore this job would work-related well in a unit that is addressing every the criter in swarm 4.G.A.

The students should try to visualize the lines of the contrary first, and also then they have the right to make or be noted with cutouts of the 4 quadrilaterals or map them top top tracing paper. It is useful for students come experiment and see what walk wrong, because that example, as soon as reflecting a rectangle (which is no a square) about a diagonal. This task helps construct visualization skills as fine as endure with various shapes and how they behave when reflected.

Students should return to this task both in center school and also in high college to analyze it indigenous a much more sophisticated perspective as they develop the tools to do so. In eighth grade, the quadrilaterals deserve to be offered coordinates and also students have the right to examine properties of reflections in the coordinate system. In high school, students can use the abstract interpretations of reflections and of the various quadrilaterals to prove that these quadrilateral are, in fact, characterized by the number of the lines of symmetry that they have.


Solution

The currently of symmetry because that each of the 4 quadrilaterals are shown below:

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When a geometric figure is folded about a line of symmetry, the two halves match up for this reason if the college student have duplicates of the quadrilaterals they have the right to test lines of symmetry by folding. Because that the square, it can be folded in half over either diagonal, the horizontal segment which cuts the square in half, or the upright segment which cut the square in half. So the square has 4 lines that symmetry. The rectangle has only two, as it have the right to be urgent in half horizontally or vertically: students need to be urged to try to wrinkles the rectangle in half diagonally to watch why this does not work. The trapezoid has actually only a vertical heat of symmetry. The parallelogram has actually no currently of the opposite and, as with the rectangle, students need to experiment v folding a copy to watch what happens through the lines through the diagonals and horizontal and also vertical lines.

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The present of symmetry indicated are the just ones because that the figures. One method to show this is to keep in mind that for a quadrilateral, a heat of symmetry need to either match two vertices on one side of the line through two vertices ~ above the other or it should pass through two of the vertices and then the other two vertices pair up as soon as folded over the line. This borders the variety of possible present of symmetry and also then experimentation will show that the only possible ones space those presented in the pictures.