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

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

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IM Commentary

This task offers students a chance to experiment v reflections of the aircraft and their impact on specific varieties of quadrilaterals. That is bothinteresting and also important that these types of quadrilaterals have the right to be distinguished by their lines that symmetry. The just pictures absent here, from this allude of view, space those of a rhombus and a general quadrilateral which does no fit into any kind of of the special categories thought about here.

This job is ideal suited for instruction return it can be adjusted for assessment. If students have actually not yet learned the terminology because that trapezoids and parallelograms, the teacher can start by explaining the definition of those terms. 4.G.2 says that students must classify figures based upon the existence or absence of parallel and also perpendicular lines, so this task would job-related well in a unit the is addressing every the criter in cluster 4.G.A.

The student should shot to visualize the currently of symmetry first, and also then they have the right to make or be noted with cutouts the the four quadrilaterals or trace them on tracing paper. The is useful for students to experiment and see what walk wrong, because that example, when reflecting a rectangle (which is no a square) about a diagonal. This activity helps develop visualization an abilities as fine as experience with various shapes and also how they behave when reflected.

Students need to return come this task both in center school and also in high college to analysis it indigenous a an ext sophisticated perspective together they construct the devices to execute so. In eighth grade, the quadrilaterals deserve to be provided coordinates and also students deserve to examine properties of reflections in the name: coordinates system. In high school, students deserve to use the abstract meanings of reflections and of the different quadrilaterals to prove the these quadrilaterals are, in fact, defined by the variety of the present of symmetry the they have.


Solution

The present of symmetry for each of the 4 quadrilaterals are presented below:

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When a geometric number is folded around a line of symmetry, the 2 halves match up so if the students have duplicates of the quadrilateral they can test present of the contrary by folding. For the square, it deserve to be folded in fifty percent over one of two people diagonal, the horizontal segment which cuts the square in half, or the upright segment which cut the square in half. So the square has 4 lines of symmetry. The rectangle has only two, together it have the right to be urgently in fifty percent horizontally or vertically: students must be urged to try to fold the rectangle in fifty percent diagonally to view why this does not work. The trapezoid has actually only a vertical heat of symmetry. The parallelogram has no currently of symmetry and, similar to the rectangle, students need to experiment v folding a copy to see what happens with the lines through the diagonals and also horizontal and also 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 note that because that a quadrilateral, a line of symmetry need to either complement two vertices ~ above one next of the line through two vertices ~ above the other or it must pass with two that the vertices and also then the other two vertices pair up as soon as folded end the line. This limits the variety of possible currently of symmetry and then trial and error will present that the only possible ones space those presented in the pictures.