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If all three sides of two triangles are identical in size and all three angles are equal in size, they are said to be congruent. To make these triangles seem the same, they can be moved around, rotated, flipped, and turned. If they’re corrected, they’ll line up. Triangles with the same sides and angles are said to be congruent. To see if two triangles are congruent, apply one of four congruency criteria. As a result, only three of the six variables can be used to determine triangle congruence. Congruence is a mathematical term that describes the similarity of two figures based on their shape and size.
Congruence of triangles meaning
Congruent refers to two shapes that share the same shape and size. When two shapes are congruent, one of their mirror images is the same as the other.
In Δ ABC & ΔDEF, as shown above, we can identify that AB = DE, AC = DF, & BC= EF and ∠A= ∠D, ∠B = ∠E and ∠C = ∠F Then we can say that Δ ABC ≅ ΔDEF.
What is CPCT
It stands for “Corresponding parts of Congruent triangles” and is mostly utilized after proving triangle congruency. By congruency, we imply that the triangles are exactly the same in terms of their sides and angles. So, we use conventional axioms to show them congruent, such as SSS, SAS, ASA, RHS, AAS, which is done by observing a certain set of corresponding angles and sides, and after that is done, the remainder of the corresponding sides and angles become equal. We put an end to it by writing CPCT.
Triangles’ Congruence Conditions
If two triangles are the same size and shape, they are said to be congruent. It is not necessary to find all six corresponding elements of both triangles to determine that they are congruent. There are five prerequisites for two triangles to be congruent, according to studies and trials. The congruence properties are SSS, SAS, ASA, AAS, and RHS.
SSS (Side-Side-Side)
If all three sides of one triangle are equal to the corresponding three sides of the second triangle, the two triangles are said to be congruent.
SAS (Side-Angle-Side)
If any two sides and the angle between the sides of one triangle are comparable to the corresponding two sides and angle between the sides of the second triangle, the two triangles are said to be congruent.
ASA (Angle-Side- Angle)
If any two angles and sides contained between the angles of one triangle are equivalent to the corresponding two angles and sides included between the angles of the second triangle, the two triangles are said to be congruent.
AAS (Angle-Angle-Side)
The abbreviation AAS stands for angle-angle-side. When two angles and a non-included side of one triangle are identical to the corresponding angles and sides of another triangle, the triangles are said to be congruent.
RHS (Right angle- Hypotenuse-Side)
If the hypotenuse and a side of one right-angled triangle are comparable to the hypotenuse and a side of the other right-angled triangle, the two right triangles are said to be congruent.
Conclusion
In this article we learn, the adjective equal is frequently used instead of congruent Two line segments are congruent if their lengths are the same. If two angles have the same measure, they are congruent. Two circles are congruent if their diameters are the same.
Humans need to understand the structure of their environment, hence congruence is an important mathematical concept. Congruence is ingrained in the daily lives of young infants, allowing them to develop intuitive senses of this geometric relationship.
