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

For each quadrilateral, find and also draw all lines that symmetry.

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## IM Commentary

This task provides students a opportunity to experiment through reflections the the plane and their influence on specific species of quadrilaterals. That is bothinteresting and important that these types of quadrilaterals have the right to be differentiated by your lines the symmetry. The only pictures lacking here, indigenous this point of view, room those that a rhombus and a basic quadrilateral i beg your pardon does not fit into any of the one-of-a-kind categories considered here.

This job is finest suited for instruction back it could be adapted for assessment. If students have actually not yet 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 have to classify figures based on the presence or absence of parallel and perpendicular lines, for this reason this job would occupational well in a unit that is addressing every the criter in cluster 4.G.A.

The college student should shot to visualize the lines of the contrary first, and also then they deserve to make or be listed with cutouts that the 4 quadrilaterals or trace them ~ above tracing paper. It is helpful for students to experiment and see what goes wrong, because that example, as soon as reflecting a rectangle (which is no a square) about a diagonal. This task helps build visualization an abilities as well as suffer with various shapes and also how lock behave as soon as reflected.

Students have to return to this job both in middle school and also in high institution to analyze it native a more sophisticated perspective as they construct the tools to execute so. In eighth grade, the quadrilaterals deserve to be provided coordinates and also students have the right to examine nature of reflect in the coordinate system. In high school, students deserve to use the abstract interpretations of reflections and of the different quadrilaterals come prove that these quadrilateral are, in fact, defined by the number of the lines of symmetry that they have.

## Solution

The currently of symmetry because that each of the four quadrilaterals are presented below:

When a geometric figure is folded around a line of symmetry, the two halves complement up so if the college student have duplicates of the square they have the right to test lines of the opposite by folding. For the square, it can be urgently in half over one of two people diagonal, the horizontal segment which cut the square in half, or the vertical segment which cuts the square in half. For this reason the square has 4 lines that symmetry. The rectangle has actually only two, together it can be urgently in half horizontally or vertically: students should be motivated to try to fold the rectangle in half diagonally to see why this does not work. The trapezoid has actually only a vertical line of symmetry. The parallelogram has no currently of the contrary and, just like the rectangle, students have to experiment v folding a copy to see what happens v the lines with the diagonals and horizontal and vertical lines.

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The currently of symmetry suggested are the only ones because that the figures. One way to show this is to note that for a quadrilateral, a heat of symmetry should either match two vertices ~ above one side of the line through two vertices on the various other or it must pass through two that the vertices and then the various other two vertices pair up once folded end the line. This borders the variety of possible present of symmetry and also then experimentation will display that the only possible ones are those presented in the pictures.