Congruence is a mathematical term which refers to the figure having same shape and size. If one thing is compared to itself then it is an obvious thing that both the variable would have the same shape and size. Likewise the geometric figures, angles, line segments and geometric shapes can possess congruence property. If two lines have the same length then both the lines are congruent in nature. If two structures have the same shape and size then both the structure are said to be congruent in nature. If the angle has been measured with the same angle then the angle is said to be congruent. In the same way if a triangle with same side length and angle measures, the triangle would be congruent.
The symbol for congruence is:
For instance, if we were looking at angle A, because of the reflexive property of congruence, we could say angle A is congruent to angle A.
More formally, two sets of points are called congruent if, and only if, one can be transformed into the other by an isometry, i.e., a combination of rigid motions, namely a translation, a rotation, and a reflection. This means that either object can be repositioned and reflected (but not resized) so as to coincide precisely with the other object. So two distinct plane figures on a piece of paper are congruent if is cut into two pieces and then match them up completely.
In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects.
Two line segments are congruent if they have the same length.
Two angles are congruent if they have the same measure.
Two circles are congruent if they have the same diameter.
In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters and areas.
The related concept of similarity applies if the objects have the same shape but do not necessarily have the same size. (Most definitions consider congruence to be a form of similarity, although minorities require that the objects have different sizes in order to qualify as similar.)
SAS (Side-Angle-Side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
SSS (Side-Side-Side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
ASA (Angle-Side-Angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.
AAS (Angle-Angle-Side): If two pairs of angles of two triangles are equal in measurement, and pair of corresponding non-included sides is equal in length, then the triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180.
RHS (Right-angle-Hypotenuse-Side), also known as HL (Hypotenuse-Leg): If two right-angled triangles have their hypotenuses equal in length, and a pair of shorter sides is equal in length, then the triangles are congruent.
There are three properties of congruence.
Reflexive property of equality
The reflexive property means comparing the quantity to itself.
If a is a number, then a = a.
Reflexive property of congruence
In geometry, the reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself.
For example: ∠A≅∠A
The symmetric property states that if one figure is congruent to another, then the second figure is also congruent to the first. For any angles A and B
For example if ∠A≅∠B, then ∠B≅∠A
Transitive property states that if two angles are both congruent to a third angle, then the first two angles are also congruent.
For any angles A, B and C if ∠A≅∠B and ∠B≅∠C, then ∠A≅∠C
The main focus of the paper is reflexive property of congruence
The reflexive property of congruence shows that any geometric figure is congruent to itself. A line segment has the same length, an angle has the same angle measure, and a geometric figure has the same shape and size as itself. The figures can be thought of as being a reflection of itself.
The reflexive property of congruence can also be demonstrated for line segments.
The line segment A ≅ B
Triangle showing congruence property.
The triangle possess the property of congruence
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