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

For each quadrilateral, find and also draw every lines the symmetry.

You are watching: What quadrilateral has no lines of symmetry

## IM Commentary

This task provides students a chance to experiment through reflections that the airplane and their influence on specific species of quadrilaterals. That is bothinteresting and also important the these varieties of quadrilaterals have the right to be distinguished by your lines that symmetry. The just pictures absent here, native this point of view, are those of a rhombus and also a basic quadrilateral i m sorry does not fit into any type of of the unique categories taken into consideration here.

This task is ideal suited for instruction return it could be adapted for assessment. If students have actually not however learned the terminology because that trapezoids and parallelograms, the teacher can begin by explaining the an interpretation of those terms. 4.G.2 says that students have to classify figures based upon the visibility or absence of parallel and perpendicular lines, so this task would job-related well in a unit the is addressing all the criter in cluster 4.G.A.

The student should try to visualize the currently of symmetry first, and also then they have the right to make or be provided with cutouts the the four quadrilaterals or trace them top top tracing paper. That is beneficial for students come experiment and also see what go wrong, because that example, when reflecting a rectangle (which is no a square) about a diagonal. This task helps construct visualization an abilities as fine as endure with various shapes and how lock behave when reflected.

Students should return to this job both in center school and in high college to analysis it indigenous a more sophisticated perspective together they build the tools to perform so. In eighth grade, the quadrilaterals have the right to be offered coordinates and also students can examine nature of reflections in the coordinate system. In high school, students have the right to use the abstract meanings of reflections and of the different quadrilaterals come prove that these quadrilaterals are, in fact, identified by the variety of the present of symmetry that they have.

## Solution

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

When a geometric number is folded about a line of symmetry, the 2 halves match up for this reason if the college student have duplicates of the quadrilateral they have the right to test present of the contrary by folding. Because that the square, it have the right to be folded in half over one of two people diagonal, the horizontal segment which cut the square in half, or the upright segment which cut the square in half. So the square has four lines of symmetry. The rectangle has actually only two, as it have the right to be urgent in half horizontally or vertically: students must be urged to try to wrinkles the rectangle in fifty percent diagonally to see why this does no work. The trapezoid has actually only a vertical line of symmetry. The parallelogram has actually no currently of the opposite and, similar to the rectangle, students must experiment v folding a copy to check out what happens through the lines v the diagonals and horizontal and vertical lines.

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The currently of symmetry indicated are the just ones for the figures. One method to display this is to note that for a quadrilateral, a line of symmetry must either enhance two vertices ~ above one next of the line v two vertices top top the other or it need to pass v two of the vertices and then the other two vertices pair up as soon as folded over the line. This limits the variety of possible lines of symmetry and also then testing will display that the only possible ones are those shown in the pictures.