Update on 2024-04-15

# Full Form of CPCT in Mathematics

When we study the congruent triangle, we come across the term CPCT. “Corresponding Parts of Congruent Triangles” is known as CPCT. Congruent triangles have equal corresponding parts, as is well known.

We frequently use the abbreviation cpct in short terms rather than the complete form while discussing triangle topics and answering inquiries.

A statement or theorem about congruent geometry is that the corresponding sections of congruent triangles are congruent (CPCTC).

Thus, The relationship between the sides and angles of two congruent triangles is referred to as "corresponding parts of congruent triangles," or cpct.

## Congruent Triangles

The most fundamental shapes we learn are triangles. Triangles are three-sided closed figures that can be classified into many forms based on their sides and angles. Equilateral, isosceles, scalene, etc., are examples of common variations.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size. You can move, flip, twist, and turn these triangles to produce the same effect.

When two figures resemble one another in terms of size and shape, this is what mathematics refers to as congruence. In essence, two triangles are congruent if and only if they follow the five congruence rules.

However, locating all six dimensions is essential. As a result, only three of the six variables can be used to evaluate the congruence of triangles. Congruent triangles have equal comparable sides and angles.

Congruence is a concept used to describe an object and its mirror image. Two things or shapes are considered to be congruent if they may be superimposed on one another.

Regarding size and shape, they are the same. In the context of geometric figures, line segments with the same length and angles with the same measure are congruent.

This indicates that either object may be precisely aligned with the other object by moving and reflecting it, but not by resizing it. So if we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are congruent. The paper may be turned over.

A triangle is a polygon with three angles made of three lines. When the side lengths and angle measurements of two triangles match, they are said to be congruent. As a result, both triangles are prepared for side-by-side and angle-to-angle superimposition.

Δ PQR and Δ LMN are congruent triangles in the aforementioned illustration. This implies,

The triangles PQR and LMN appear to be congruent triangles in the image above, as can be seen. This indicates that the related vertices, P = L, Q = M, and R = N, are identical. Additionally, their sides are identical (PR = LN, PQ = LM, and QR = MN).

Triangles that have comparable sides and equal angles are said to be congruent. Indicating congruence is the sign ". As seen in the example above, PQR ≅ LMN can be written. They share a common space and perimeter.

## CPCT Mathematical Rules

Corresponding portions of Congruent triangles are the complete form of CPCT. Triangles can be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles.

The following are many congruency rules:

• ASA (Angle-Side-Angle)
• AAS (Angle-Angle-Side)
• RHS (Right Angle-Hypotenuse-Side)
• SSS (Side-Side-Side)
• SAS (Side-Angle-Side)

### Congruent Triangles: Properties

• ASA (Angle-Side-Angle)

The two triangles are said to be congruent by the ASA (Angle-Side-Angle) rule if any two angles and the side included between the angles of one triangle are comparable to the corresponding two angles and the side included between the angles of the next triangle.

• AAS (Angle-Angle-Side)

Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of 2nd triangle.

• RHS (Right Angle-Hypotenuse-Side)

The two right triangles are said to be congruent by the RHS rule if the hypotenuse and a side of one right-angled triangle are equal to the hypotenuse and a side of the second right-angled triangle.

• SSS (Side-Side-Side)

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the next triangle.

• SAS (Side-Angle-Side)

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of another triangle.

FAQ’s

Q1. What is the full form of cpct in mathematics?

Ans. The relationship between the sides and angles of two congruent triangles is referred to as "corresponding parts of congruent triangles," or cpct.

Q2. What are the corresponding parts of congruent triangles?

Ans. Corresponding portions of Congruent triangles are the complete form of CPCT. Triangles can be shown to be congruent after which the final dimension can be anticipated without actually measuring the triangle's sides and angles.

Q3. What criteria are there for a triangle's congruence?

Ans. The SAS, SSS, ASA, AAS, and HL tests for congruence in a triangle are available. These tests provide information on the several permutations of congruent angles and/or sides that aid in assessing whether the two triangles are congruent.

Q4. Explain the Side-Side-Side Theorem.

Ans. According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the next triangle.

Q5. Explain the SAS (Side-Angle-Side) Theorem.

Ans. According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the other triangle.