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

For every quadrilateral, find and draw all lines the symmetry.

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## IM Commentary

This task offers students a chance to experiment with reflections that the airplane and their influence on specific species of quadrilaterals. That is bothinteresting and important the these varieties of quadrilaterals can be identified by their lines that symmetry. The only pictures missing here, from this suggest of view, space those of a rhombus and a general quadrilateral which does not fit into any of the distinct categories considered here.

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

The students should shot to visualize the present of the contrary first, and also then they can make or be provided with cutouts of the 4 quadrilaterals or map them top top tracing paper. It is beneficial for students to experiment and also see what goes wrong, for example, once reflecting a rectangle (which is not a square) about a diagonal. This task helps construct visualization skills as well as endure with different shapes and also how lock behave as soon as reflected.

Students need to return come this job both in middle school and in high institution to analysis it indigenous a much more sophisticated perspective together they develop the tools to execute so. In eighth grade, the quadrilaterals have the right to be offered coordinates and also students have the right to examine nature of reflect in the coordinate system. In high school, students can use the abstract meanings of reflections and of the various quadrilaterals come prove that these quadrilaterals are, in fact, defined by the number of the present of symmetry the they have.

## Solution

The present of symmetry for each of the four quadrilaterals are presented below:

When a geometric figure is folded around a heat of symmetry, the two halves complement up therefore if the students have copies of the quadrilaterals they have the right to test currently of symmetry by folding. Because that the square, it can be urgent in half over one of two people diagonal, the horizontal segment which cuts the square in half, or the vertical segment which cut the square in half. For this reason the square has 4 lines of symmetry. The rectangle has only two, as it can be urgently in fifty percent horizontally or vertically: students have to be urged to shot to fold the rectangle in half diagonally to watch why this does no work. The trapezoid has only a vertical line of symmetry. The parallelogram has no present of the opposite and, as with the rectangle, students should experiment v folding a copy to view what happens through the lines through the diagonals and horizontal and vertical lines.

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The lines of symmetry shown are the just ones because that the figures. One method to present this is to keep in mind that because that a quadrilateral, a heat of symmetry need to either match two vertices on one next of the line with two vertices ~ above the various other or it have to pass through two the the vertices and then the various other two vertices pair up when folded over the line. This limits the variety of possible present of symmetry and also then trial and error will present that the only feasible ones room those displayed in the pictures.