Question

4) Explain the difference between symmetry and congruency.

Answer 1

Answer:

Two figures are congruent if they can be superimposed so that they fit exactly. It can be shown that two plane polygons are congruent if and only if a one-to-one correspondence can be established between them such that corresponding sides have the same length and corresponding angles have the same measure.

Thus, figures that are the same size and shape are congruent. Corresponding parts of congruent figures are congruent. Congruent figures, such as those below, may be in different positions.

Congruent shapes

A figure has line symmetry if it can be folded in half and the two halves are congruent. The line made by the fold is the line of symmetry. Line symmetry is also called bilateral symmetry. Figures can have no lines of symmetry or an unlimited number of lines of symmetry.

Step-by-step explanation:

Answer 2

The difference between congruent and similarity can be understood through the world of mathematics.  Shape, proportion and angles all play their part in defining these two words.

Congruent shapes have identical measurements and coincide with each other when superimposed. Two congruent objects are the same size and shape, but their orientation or placing in a space can be different.  This does not change the fact that they are the same because they possess the same physical properties, the same angles as well as the same measurements.

Similarity means closely resembling each other but not quite the same.  Mathematically a shape can be similar in its basic shape, a circle for example, but different in size.  The difference in size aspect means that a similar shape can never be congruent.

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