Congruence of Plane Figures

If two objects are of exactly the same shape and size, they are said to be congruent. The relation between two congruent objects being congruent is called congruence.

A plane figure is any shape that can be drawn in two dimensions e.g. rectangle, square, triangle, rhombus, etc. To check if two figures drawn on a paper are congruent, make a traced copy of one of the figures on a tracing paper and place it over the other. The other method is to cut out one of these figures and place it over the other. However, care should be taken not to twist, bend or stretch the traced or cut image.

The method of superposition examines the congruence of plane figures, line segments and angles. Two plane figures are congruent if each, when superimposed on the other, covers it exactly. Congruence is denoted by ≅.
e.g. Two plane figures, say, P1 and P2, are congruent if the trace copy of P1 fits exactly on that of P2.  We write P1 ≅ P2

If two line segments have the same or equal length, they are congruent. Also, if two line segments are congruent, then they have the same length.
e.g. Two line segments, say, AB _  and EF _  are congruent if they have equal lengths. We write this as AB _  ≅ EF _ or AB = EF.



If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are the same. If two angles are congruent, then the lengths of their arms do not matter.
e.g. Two angles, say, ∠PQR and ∠XYZ, are congruent if their measures are equal.  We write this as ∠PQR ≅ ∠XYZ or as ∠PQR = ∠XYZ.  However, commonly, we write ∠PQR ≅ ∠XYZ.


Two circles of equal radii are congruent. Two squares of equal sides are congruent.

Summary

If two objects are of exactly the same shape and size, they are said to be congruent. The relation between two congruent objects being congruent is called congruence.

A plane figure is any shape that can be drawn in two dimensions e.g. rectangle, square, triangle, rhombus, etc. To check if two figures drawn on a paper are congruent, make a traced copy of one of the figures on a tracing paper and place it over the other. The other method is to cut out one of these figures and place it over the other. However, care should be taken not to twist, bend or stretch the traced or cut image.

The method of superposition examines the congruence of plane figures, line segments and angles. Two plane figures are congruent if each, when superimposed on the other, covers it exactly. Congruence is denoted by ≅.
e.g. Two plane figures, say, P1 and P2, are congruent if the trace copy of P1 fits exactly on that of P2.  We write P1 ≅ P2

If two line segments have the same or equal length, they are congruent. Also, if two line segments are congruent, then they have the same length.
e.g. Two line segments, say, AB _  and EF _  are congruent if they have equal lengths. We write this as AB _  ≅ EF _ or AB = EF.



If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are the same. If two angles are congruent, then the lengths of their arms do not matter.
e.g. Two angles, say, ∠PQR and ∠XYZ, are congruent if their measures are equal.  We write this as ∠PQR ≅ ∠XYZ or as ∠PQR = ∠XYZ.  However, commonly, we write ∠PQR ≅ ∠XYZ.


Two circles of equal radii are congruent. Two squares of equal sides are congruent.

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