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

For every quadrilateral, find and also draw every lines that symmetry.

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## IM Commentary

This task provides students a opportunity to experiment through reflections of the aircraft and their impact on specific types of quadrilaterals. It is bothinteresting and important the these varieties of quadrilaterals deserve to be differentiated by your lines the symmetry. The only pictures absent here, from this suggest of view, room those that a rhombus and a basic quadrilateral i beg your pardon does no fit into any of the one-of-a-kind categories taken into consideration here.

This job is best suited because that instruction although it can be adjusted for assessment. If students have actually not however learned the terminology for trapezoids and also parallelograms, the teacher can begin by explaining the meaning of those terms. 4.G.2 states that students have to classify figures based upon the presence or lack of parallel and perpendicular lines, so this task would work-related well in a unit that is addressing every the criter in cluster 4.G.A.

The student should try to visualize the lines of symmetry first, and then they can make or be detailed with cutouts the the 4 quadrilaterals or map them top top tracing paper. The is useful for students come experiment and also see what go wrong, for example, as soon as reflecting a rectangle (which is no a square) around a diagonal. This activity helps develop visualization an abilities as fine as suffer with different shapes and also how they behave once reflected.

Students must return come this task both in middle school and in high institution to analyze it from a an ext sophisticated perspective as they build the devices to execute so. In eighth grade, the quadrilaterals have the right to be provided coordinates and also students have the right to examine properties of reflections in the coordinate system. In high school, students have the right to use the abstract definitions of reflections and of the various quadrilaterals to prove the these quadrilaterals are, in fact, defined by the variety of the currently of symmetry that they have.

## Solution

The currently of symmetry for each that the four quadrilaterals are shown below:

When a geometric figure is folded about a heat of symmetry, the two halves match up so if the students have copies of the quadrilaterals they have the right to test lines of the opposite by folding. For the square, it can be urgently in fifty percent over either diagonal, the horizontal segment which cuts the square in half, or the vertical segment which cuts the square in half. So the square has four lines that symmetry. The rectangle has actually only two, together it can be urgently in half horizontally or vertically: students must be urged to try 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 symmetry and, just like the rectangle, students need to experiment through folding a copy to view what happens v the lines v the diagonals and also horizontal and vertical lines.

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The present of symmetry shown are the just ones for the figures. One method to show this is to keep in mind that because that a quadrilateral, a heat of symmetry must either complement two vertices top top one side of the line v two vertices ~ above the various other or it need to pass with two the the vertices and then the various other two vertices pair up once folded over the line. This borders the variety of possible present of symmetry and also then testing will present that the only feasible ones are those shown in the pictures.