The lines of symmetry in a quadrilateral are the imaginary lines passing through the center of the quadrilateral. They divide the quadrilateral into similar halves.

How Many Lines of Symmetry Does a Quadrilateral Have

Concept: As we know, a quadrilateral is any shape having four sides, it does not have a fixed number of symmetrical lines for all its shapes. However, we can determine the number of lines of symmetry for any quadrilaterals by folding that shape along the lines such that the resulting shapes are identical halves of the original figure.

Explanation: For example, take a square and fold the shape over any of its diagonal, the horizontal segments, and the vertical segments. We will get four such lines in a square that divide the square into similar halves. Thus a square has four lines of symmetry. Similarly, a rectangle has only two lines of symmetry, as we can fold it either horizontally or vertically. Try to fold the rectangle over any of its diagonals. What have you found?

Repeat the above procedure for all other special quadrilaterals such as parallelogram, rhombus, trapezoid, and kite and note the results. Does your result match with the results given above?

FAQs

Q1. What quadrilateral has no lines of symmetry?

Ans. Parallelogram is a quadrilateral with no lines of symmetry.

Q2. What quadrilaterals have two lines of symmetry?

Ans. Rectangle and rhombus have exactly two lines or symmetry.

Q3. What quadrilateral has four lines of symmetry?

Ans. Square is the quadrilateral that has four lines of symmetry.

Q4. Which quadrilaterals have diagonals that are not lines of symmetry?

Ans. Parallelogram and trapezoid (except isosceles trapezoid) have diagonals that are not lines of symmetry.

Q5. What quadrilateral has one line of symmetry but no rotational symmetry?

Ans. Kite is the quadrilateral with one line of symmetry but no rotational symmetry.

Q6. What quadrilateral has a horizontal line of symmetry but no vertical line of symmetry?

Ans. Kite is the quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.

Q7. Name a quadrilateral with both horizontal and vertical lines of symmetry?

Ans. Rectangle

Q8. How many lines of symmetry does an irregular quadrilateral have?

Ans. An irregular quadrilateral has no lines of symmetry.

Q9. How many lines of symmetry does a regular quadrilateral have?

Ans. Square being the only regular quadrilateral it has four lines of symmetry.

Q10. What quadrilateral has only one line of symmetry?

Ans. An isosceles trapezoid has only one line of symmetry.