ABCD is a quadrilateral in which \(AB=BC\) and \(CD=AD\). This quadrilateral has:
One line of symmetry BD
Since \(AB = BC\), point B is equidistant from A and C, and since \(CD = AD\), point D is also equidistant from A and C.
Both B and D therefore lie on the perpendicular bisector of AC, which makes BD the axis of symmetry of this quadrilateral (a kite shape).
Reflecting the figure across BD maps A onto C and leaves B and D fixed, so the whole quadrilateral maps onto itself; no other line does this since AB is not generally equal to AD.
Hence, the quadrilateral has one line of symmetry, BD.
Similar Questions
Some of the English letters depicts symmetrical structures. Which one of the following structures of letters has not linear symmetry about both horizontal and vertical axes ?
Important Questions from Symmetry and Reflection
Number of lines of symmetry in a square is -
The curve given by xy = 15 is symmetrical about what?
- Which of the following letters does not have rotational symmetry?
- Nitu is always confused in identifying the transformations. Her mathematics teacher helped her by giving one simple word for each transformation namely : Reflection, Rotation, Translation and Enlargement.
Which of the following represents the correct sequence of meaning of each transformation as given above?
(1) Flip, Slide, Turn and Bigger Figure
(2) Turn, Slide, Flip and Bigger Figure
(3) Flip, Turn, Slide and Bigger Figure
(4) Slide, Flip, Turn and Bigger Figure - Which of the following has/have only two lines of symmetry?
A. Equilateral triangle
B. Rectangle
C. Rhombus
D. Isosceles triangle
Choose the correct option.
