CPCT full form in maths is corresponding parts of congruent triangles. The corresponding sides of a congruent triangle or cpct tell us that two triangles whose congruent sides and corresponding angles are equal.
The term “corresponding parts of congruent triangles,” or “cpct,” refers to the relationship between the sides and the angles of two congruent triangles.
CPCT Full Form In Maths – Corresponding Parts of Congruent Triangles
CPCT is an abbreviation for “Corresponding parts of Congruent triangles” in mathematics. It is mainly used after proving triangle congruence. By congruence, we mean that both triangles are exactly the same on all sides and angles. Then, using conventional axioms such as SSS, SAS, ASA, RHS, and AAS, we establish that they are congruent by observing a certain set of corresponding angles and sides, and once that is done, the remainder of the corresponding sides and angles become equal.
If there are two triangles are congruent by any of the following laws of congruence, their corresponding sides and angles must be equal.
- SSS (Side-Side-Side)
- SAS (Side-Angle-Side)
- ASA or AAS (Angle-Side-Angle)
- RHS (Right angle-Hypotenuse-Side)
Let us take for example that two triangles ΔABC ≅ ΔPQR, by any of the above congruence rules, then
The corresponding parts of a congruent triangle are equal.
The corresponding parts of both the triangles are:
Thus, the corresponding parts of a congruent triangle are equal.
Application of CPCT
The concept of CPCT (Corresponding Parts of Congruent Triangles) has practical applications. Congruent triangles are used in many industries, including engineering, architecture, and construction, to ensure precision in measurements and design. Engineers verify that the matching sides of particular triangles have the same lengths when constructing bridges or buildings to ensure stability and balance.
CPCT can also be used in land surveying to precisely measure and divide lthe and. It also finds application in computer graphics and animation to modify shapes and objects and change their proportions while maintaining congruence.