# Parallelogram lines of symmetry

A parallelogram is a type of quadrilateral where the opposite sides are parallel and equal, **parallelogram lines of symmetry**. The imaginary line so formed along which you can fold a figure to obtain the symmetrical halves is referred to as the line of symmetry. Thus, the lines of symmetry of a parallelogram refer to the lines cutting the parallelogram into two identical parts.

General parallelogram has no lines of symmetry. Some specific types of parallelogram do. See below. Rhombus is a special type of parallelogram and it has two lines of symmetry - its diagonals. Rectangle, which is not a square, has two lines of symmetry - two lines going through the midpoints of opposite sides.

## Parallelogram lines of symmetry

Below are pictures of four quadrilaterals: a square, a rectangle, a trapezoid and a parallelogram. This task provides students a chance to experiment with reflections of the plane and their impact on specific types of quadrilaterals. It is both interesting and important that these types of quadrilaterals can be distinguished by their lines of symmetry. The only pictures missing here, from this point of view, are those of a rhombus and a general quadrilateral which does not fit into any of the special categories considered here. This task is best suited for instruction although it could be adapted for assessment. If students have not yet learned the terminology for trapezoids and parallelograms, the teacher can begin by explaining the meaning of those terms. The students should try to visualize the lines of symmetry first, and then they can make or be provided with cutouts of the four quadrilaterals or trace them on tracing paper. It is useful for students to experiment and see what goes wrong, for example, when reflecting a rectangle which is not a square about a diagonal. This activity helps develop visualization skills as well as experience with different shapes and how they behave when reflected. Students should return to this task both in middle school and in high school to analyze it from a more sophisticated perspective as they develop the tools to do so. In eighth grade, the quadrilaterals can be given coordinates and students can examine properties of reflections in the coordinate system.

Below are explanations of the symmetry lines *parallelogram lines of symmetry* each of these parallelograms. Rhombus is a unique kind of parallelogram and it has 2 lines of symmetry - its diagonals. Rhombus 2 Both its diagonals dividing it into two identical halves.

August 12, by Anthony Persico. Every Geometry class or course will include a deep exploration of the properties of parallelograms. In this post, we will quickly review the key properties of parallelograms including their sides, angles, and corresponding relationships. Finally, we will determine whether or not a parallelogram has line symmetry. And, if a parallelogram has line symmetry, what would parallelogram lines of symmetry look like in the form of a diagram.

A parallelogram is a type of quadrilateral where the opposite sides are parallel and equal. The imaginary line so formed along which you can fold a figure to obtain the symmetrical halves is referred to as the line of symmetry. Thus, the lines of symmetry of a parallelogram refer to the lines cutting the parallelogram into two identical parts. Also, the lines of symmetry in a parallelogram vary as per the type of parallelogram. The lines of symmetry in a parallelogram are those lines that divide a parallelogram into two halves such that each half is the mirror image of the other. We know that there are different parallelograms categorized as per their shapes , the line segments, and corners they are made up of. Thus, these have different lines of symmetry and different numbers of symmetry lines.

### Parallelogram lines of symmetry

Lines of symmetry in a parallelogram vary from type to type. In simple words, the parallelogram lines of symmetry refer to the lines which cut the parallelogram into two identical parts. To recall, a parallelogram is a quadrilateral 4-sided figure where the opposite sides are parallel to each other. The lines of symmetry are those lines which divide a parallelogram into two halves where each half is the mirror image of the other. Different parallelograms have different lines of symmetry and the different number of symmetry lines. There are three types of a parallelogram whose number of symmetry lines are given in the aforementioned table. Below are the explanations on the lines of symmetry in each of these parallelograms. In a square, there are four lines of symmetry, each of which divides it into two identical parts.

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Parallelograms vary in their shape and so do their lines of symmetry as well. Subscribe Now. Parallelogram Number of symmetry lines Symmetry lines Square 4 Both its diagonals and the lines joining the midpoints of its opposite sides, that is the bisectors. JEE Advanced Syllabus. Multiplying Fractions. You can often find me happily developing animated math lessons to share on my YouTube channel. A quadrilateral is any solid shape with four straight sides. Frequently asked questions. Finally, we will determine whether or not a parallelogram has line symmetry. One way to show this is to note that for a quadrilateral, a line of symmetry must either match two vertices on one side of the line with two vertices on the other or it must pass through two of the vertices and then the other two vertices pair up when folded over the line. As a result, they have different symmetry lines and a different number of symmetry lines.

Online Math Solver. A parallelogram is a four-sided shape with opposite sides that are parallel.

What Are Perpendicular Lines. The area is bisected by Any of the lines passing through the centre of a parallelogram. Zero Vector A zero vector is defined as a line segment coincident with its beginning and ending points. Lines of symmetry in a parallelogram vary from type to type. Thus, these have different lines of symmetry and different numbers of symmetry lines. Parallelogram Number of symmetry lines Symmetry lines Square 4 Both its diagonals and the lines joining the midpoints of its opposite sides, that is the bisectors. Math worksheets and visual curriculum. In Euclidean geometry, a parallelogram is a quadrilateral with two pairs of parallel sides with the opposite sides being equal in length and the opposite angles being equal in measure. Solution: We know that a rhombus has 4 equal sides but what about diagonals? Symmetry Lines in Different Parallelograms Different parallelograms are varied in their shape and so do their lines of symmetry. Thus, it is important to check whether the lines of symmetry divide the figure not only in equal parts but as mirror images also. There are 3 types of symmetry which are as follows The line of symmetry is the imaginary line formed as a result of folding a figure to obtain the symmetrical halves. Share via. Our Journey.

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