Geometry Congruence

Definition for geometry congruence:

In Geometry, we study different figure, their properties the relations between them. Every figure has its shape, size and Position. Given two figures you can easily decide whether they are of the same shape.

Figures having same shape and size  and angles are called congruent. Congruent means equal in all respects of the given figure. If two figures are congruent then it means that the size, shape and measurement of the first figure correspond to the size, shape and measurements of the second figure. I like to share this Symbol for Congruence with you all through my article.


Congruence for geometry:


If two persons compare the size shape of their fore-hands, they will do so by comparing thumb with thumb, fore-finger with fore-finger etc. Thus thumb corresponds to thumb. Similarly the two fore-fingers correspond to each other.

When we put a figure on another figure in such a way that the first figure covers the other figure completely i.e. all parts of the first figure completely cover the corresponding parts of the other. Then these figures will be said to be congruent to each other.

The relation property of two figures being congruent is called congruence. When two figures are congruent we denote them symbolically as. One figure ≅ second figure. The property of congruence, as you know is symbolically represented as ≅.


Important points in congruence of geometry:


Congruency in geometry means to be equal in all respect.
Two figures can be said to be congruent only when all parts of one are equal to the corresponding parts of the other.
The property of congruence of figures is called congruency.
If two line segments are congruent then they must have the same length.
If two angles are congruent then their measures must be equal.
Two triangles are congruent only
Two squares are congruent if they have the same side length.
Two rectangles are congruent if they have the same length and breadth.
Two circles are congruent if they have the same radius.
Sum of the three angles of a triangle is equal to 1800 therefore. if the measures of any two of them are given the third can be ascertained.

Example of Congruence

Introduction to congruence:

Two objects are congruent if they consist of the similar shape with size. The given two triangles are congruent if their equivalent sides are equal within length also their equivalent angles are the same in size. Assume the triangles DEF and RST is congruent. These can be written as ? DEF ? ? RST. In geometry two congruent triangles contains the equal corresponding angles.

Example of Congruence

The followings are the important congruence test

ASA congruence

The two angles with the integrated faces of one triangle are equal to the corresponding two angles with the integrated faces of another triangle.

SAS congruence

The two faces with the included angle of triangle are the same to two faces with the included angle of another triangle.

AAS congruence

The two angles along throughout a non integrated side of one triangle are congruent to the identical measurements of a different triangle.

SSS congruence

Three sides of one triangle are identical to corresponding three sides of another triangle.

Example

Consider the following two triangles.




The triangle IJK is congruent to the triangle LMN

Angle I = Angle L

Angle J = Angle M

Angle K = Angle N

Length IJ = Length LM

Length JK = Length MN

Length KI = Length LN

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Examples for Congruence

Example 1 for congruence

In the following triangles are congruent then find the length of sides a, b, c.



Solution

The given triangles are congruent. Therefore the lengths of the sides of the triangles are equal.

Length EG = 52

Therefore the length VT = a = 52

Length FG = 48

Therefore the length UT = b = 48

Length EF = 50

Therefore the length UV = c = 50

Thus the a = 52, b = 48, c = 50.

Example 2 for congruence

Prove that triangle LMN is congruent to triangle PQR.



Solution

Given figure the angle L and angle P are the same.

Angle L = Angle P = 75 degree

Given figure the angle N and angle Q are the same.

Angle N = Angle Q = 65 degree.

Line segment LM is equal to the line segment PR.

Line LM = Line PR = 40 cm.

Therefore ? LMN and ? PQR are congruent through AAS congruence.