How Many Lines of Symmetry in an Isosceles Trapezium

Introduction

One line of symmetry runs through the intersections of the parallel lines in an isosceles trapezium. A trapezium is a two-dimensional quadrilateral whose one pair of opposite sides are parallel. Two sides are said to be parallel if they do not ever intersect each other. An isosceles trapezium is one in which the unparallel sides are equal in length.

When a line divides a figure into two parts such that the first one is the mirror image of the second then that line is known as the Line of Symmetry. A figure could have one or more than one lines of symmetry. In the case of an isosceles trapezium, the number of lines of symmetry will be one. This line divides the trapezium into two parts which are mirror images of each other. These two parts act as two separate trapeziums. These trapeziums are not isosceles anymore.

Symmetry in an Isosceles Trapezium

In an isosceles trapezium, if it gets divided by a line which is perpendicular to the parallel sides of the trapezium and passes through the midpoints of parallel lines, then it will divide the trapezium into two equal parts. These parts will be symmetric in nature. If a mirror is placed on the symmetric line then an image of the other part will produce in the mirror. If we draw a line parallel to the parallel lines of this trapezium, the obtained parts will not be mirror images of each other, they will be unequal. Hence, only one symmetric line can be present in an Isosceles Trapezium.

1. One pair of sides are parallel.

2. The non-parallel sides are equal in length.

3. The length of the diagonals is equal.

4. Base angles are equal.

5. The sum of opposite angles is equal to 180 degrees.

6. This type of trapezium can be inscribed in a circle.

7. The diagonals divide each other into equal halves.

Area of Isosceles Trapezium

If we consider an Isosceles Trapezium having the length of the parallel sides as a and b respectively and a distance of h between the parallel set of lines then the area can be given the following expression-

A = \frac{1}{2} (a+b) \times h

Perimeter of Isosceles Trapezium

If we consider an Isosceles Trapezium having the length of the parallel sides as a and b respectively and the length of non-parallel equal sides as c then the perimeter can be given by the following expression-

P = a + b + 2 \times c

Conclusion

An isosceles trapezium can have only one line of symmetry perpendicular to the parallel sides and passes through the midpoint of the parallel sides.