In fact, a shape can have multiple lines of symmetry. If parallelograms do not have lines of symmetry, then why doesn’t a parallelogram have lines of symmetry?įor starters, let's note that a line of symmetry is an axis or imaginary line that can pass through the center of a shape (facing in any direction) such that it cuts the shape into two equal halves that are mirror images of each other.įor example, a square, a rectangle, and a rhombus all have line symmetry because at least one imaginary line can be drawn through the center of the shape that cuts it into two equal halves that are mirror images of each other. What is the number of lines of symmetry in a parallelogram? Now that you understand the key properties and angle relationships of parallelograms, you are ready to explore the following questions: The following diagram illustrates these key properties of parallelograms:
And any pair of adjacent interior angles in a parallelogram are supplementary (they have a sum of 180 degrees). And, if a parallelogram has line symmetry, what would parallelogram lines of symmetry look like (in the form of a diagram).īefore we answer these key questions related to the symmetry of parallelograms, lets do a quick review of the properties of parallelograms: What is a parallelogram?ĭefinition: A parallelogram is a special kind of quadrilateral (a closed four-sided figure) where opposite sides are parallel to each other and have equal length.įurthermore, the interior opposite angles in any parallelogram have equal value. In this post, we will quickly review the key properties of parallelograms including their sides, angles, and corresponding relationships.įinally, we will determine whether or not a parallelogram has line symmetry. This formula is a result of dividing a trapezoid into a two triangles $ AED$ and $ BCF$, and a rectangle $ EFCD$.Every Geometry class or course will include a deep exploration of the properties of parallelograms. The same that goes for a rhombus works on a parallelogram, the area of a parallelogram is a product of its one side and altitude on that side.Īrea of a trapezoid is equal to one half of a product of sum of its bases and altitude. If we ‘translate’ triangle $ECB$ onto triangle $E’DA$ we will get a rectangular with one side $a$ and other $h$. What they have in common is that in every quadrilateral the sum of the measures of all interior angles is equal to $ 360^$ into point $A$, and extend side $ED$ over vertex $D$, we will get triangle $E’DA$ which is congruent with triangle $ECB$. It doesn’t have to form an identifiable shape. As long as the four sides connect with straight lines, it is a quadrilateral. Quadrilateral shapes include square, rectangle, trapezoid, rhombus, parallelogram, and kite (also called a tangential quadrilateral). They can be sorted into specific groups based on lengths of their sides or measures of their angles. All quadrilaterals have exactly four sides and four angles.
They are part of a plane enclosed by four sides (quad means four and lateral means side).
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