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Identifying Lines of Symmetry

In this article shall we discuss about identifying lines of symmetry. In our daily life we see many things which attract us. The attraction is due toevenness or the uniformity of the things. Such qualities add beauty tothe eyes of the observation. The quality of evenness in the shape of the things is known as symmetry. For example cut an orange into two equal halves. We observe that the two parts are symmetry.


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Introduction to identifying lines of symmetry:

Insimple, if we need to check whether any two plane surfaces are symmetry, place one above the other. If it coincides perfectly then the two objects are symmetrical. Let us learn how to find the lines of symmetry of an equilateral triangle , isosceles triangle and a line segment.


Identifying lines of symmetry of a triangle:


Consideran equilateral or isosceles triangle ABC. Let us identify the line of symmetry for this triangle. We have to find the lines of symmetry such that the line divides the triangle into two equal halves.

Case1:

Equilateral triangle: Aequilateral triangle has three sides equal. So, a line of symmetry could be drawn from any vertex and it should pass through the mid point of the side which is opposite to the vertex from where we start drawing the line.

Case 2:

Identifyinglinesofsymmetryintriange

Isosceles triangle: An isosceles triangle has two sides equal. In the following diagram AB =AC. For an isosceles triangle always drop the line from the vertex thatis between the equal sides and to the mid point of the side which is opposite to the vertex from where we start drawing the line. So, AD is the line of symmetry.

Case 3:

Scalene triangle: We could not draw lines of symmetry since all the sides of scalene triangle are different.


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Identifying lines of symmetry of a line:


Take two points A, A’ on a sheet of tracing paper and join AA’. Draw the perpendicular bisector l of the line segment AA’ bisecting it at M. Now fold the paper about l what do you observe?

 You would observe that line l is the axis of symmetry for the two points A and A’ Also, then we say that A’ is symmetric to A with respectto l or A is symmetric to A’ with respect to l.

Take a point P on the line of symmetry of A and A’ Folding the paper about l we find A coincides with A’ and P coincides with P itself. Therefore P A="PA’." It can be expressed in other words.

Identifyinglinesofsymmetryfortwopoints

Now, draw a line l and take a point Q not on l. How to locate a point Qsymmetric to Q’ with respect to l Draw the line segment QN, perpendicular to l meeting it at N. Produce QN to Q such that QN = NQ, Then is the perpendicular bisector of line segment

 QQ’ and hence Q’ is symmetric to Q with respect to l? This is the essence in method of construction by which we complete a symmetric figure when the line of symmetry and one half figures is given.

  Identifyinglinesofsymmetryfigure