Congruency of Triangles – How will you know that a Triangle is Congruent?

Congruent Triangles Properties and CPCT Rules

Congruency of Triangles – How will you know that a Triangle is Congruent.

There are three main properties of congruent triangles:

– Sides are congruent
– Angles are congruent
– Congruent triangles have the same shape

There is a specific set of rules which can be used to determine if two triangles are congruent – these are called the Congruent Triangle Postulate (CPCT) rules.

The CPCT rules are:

– If two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle, then the triangles are congruent.

– If two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle, then the triangles are congruent.

– If the three angles of one triangle are congruent to the three angles of the other triangle, then the triangles are congruent.

How Will You Know That a Triangle is Congruent?

There are three ways to determine if two triangles are congruent:

1. SSS (Side-Side-Side): This is the most basic way to determine if two triangles are congruent. If all three sides of one triangle are the same length as the corresponding sides of another triangle, the triangles are congruent.

2. SAS (Side-Angle-Side): If two sides and the angle between them of one triangle are the same length as the corresponding sides and angle of another triangle, the triangles are congruent.

3. AAS (Angle-Angle-Side): If two angles and the side between them of one triangle are the same size as the corresponding angles and side of another triangle, the triangles are congruent.

CPCT Rules in Maths

The Central Board of Secondary Education (CBSE) has prescribed the Common Core Curriculum for Classes I-XII. The Common Core Curriculum is a framework that prescribes the essential skills and knowledge that students must acquire in each grade.

The Common Core Curriculum is designed to ensure that all students in India receive a quality education and are on track to college and career readiness. The Common Core Curriculum is based on the best practices from around the world and is aligned with the latest research on how students learn.

The Mathematics strand is divided into the following modules:

Number Sense and operations
Algebra
Geometry
Measurement
Data Analysis and Probability

Let Us Learn All Three Conditions of Congruence of Triangles Class 7 CBSE in Detail.

There are three conditions of congruence of triangles:

1. Side-Side-Side (SSS)
2. Angle-Side-Angle (ASA)
3. Angle-Base-Angle (ABA)

Condition 1: Side-Side-Side (SSS)

The three sides of two triangles are congruent if and only if the corresponding angles are congruent.

Condition 2: Angle-Side-Angle (ASA)

The two angles on the same side of the line containing the two triangles’ hypotenuses are congruent, and the two triangles are congruent if and only if the corresponding sides are congruent.

Condition 3: Angle-Base-Angle (ABA)

The two angles opposite the common side are congruent, and the two triangles are congruent if and only if the corresponding sides are congruent.