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

For each quadrilateral, discover and draw all lines of symmetry.

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## IM Commentary

This task offers students a chance to experiment via reflections of the airplane and also their influence on particular forms of quadrilaterals. It is bothinteresting and crucial that these forms of quadrilaterals deserve to be distinguimelted by their lines of symmetry. The just images absent here, from this allude of see, are those of a rhombus and also a general quadrilateral which does not fit into any type of of the distinct categories thought about here.

This task is best suited for instruction although it can be adjusted for assessment. If students have actually not yet learned the terminology for trapezoids and parallelograms, the teacher can start by explaining the definition of those terms. 4.G.2 states that students need to classify numbers based upon the presence or absence of parallel and perpendicular lines, so this job would work well in a unit that is addressing all the requirements in cluster 4.G.A.

The students need to attempt to visualize the lines of symmeattempt first, and then they have the right to make or be provided via cutouts of the 4 quadrilaterals or trace them on tracing paper. It is useful for students to experiment and also view what goes wrong, for instance, as soon as reflecting a rectangle (which is not a square) around a diagonal. This activity helps develop visualization skills and also suffer with various shapes and exactly how they behave actually once reflected.

Students must go back to this job both in middle school and also in high institution to analyze it from a more sophisticated perspective as they develop the devices to execute so. In eighth grade, the quadrilaterals deserve to be provided collaborates and also students can study properties of reflections in the coordinate device. In high school, students have the right to use the abstract meanings of reflections and of the different quadrilaterals to prove that these quadrilaterals are, in reality, characterized by the variety of the lines of symmeattempt that they have.

## Solution

The lines of symmeattempt for each of the 4 quadrilaterals are shown below:

When a geometric number is folded about a line of symmetry, the 2 halves enhance up so if the students have duplicates of the quadrilaterals they deserve to test lines of symmeattempt by folding. For the square, it deserve to be folded in half over either diagonal, the horizontal segment which cuts the square in fifty percent, or the vertical segment which cuts the square in half. So the square has four lines of symmetry. The rectangle has only 2, as it deserve to be folded in half horizontally or vertically: students have to be encouraged to attempt to fold the rectangle in half diagonally to watch why this does not job-related. The trapezoid has actually only a vertical line of symmetry. The parallelogram has actually no lines of symmeattempt and, as with the rectangle, students have to experiment through folding a copy to view what happens with the lines via the diagonals and horizontal and vertical lines.

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The lines of symmetry shown are the only ones for the numbers. One way to present this is to note that for a quadrilateral, a line of symmetry must either match 2 vertices on one side of the line with two vertices on the other or it should pass via 2 of the vertices and also then the various other two vertices pair up once folded over the line. This boundaries the number of feasible lines of symmeattempt and also then testing will display that the just feasible ones are those presented in the pictures.