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Home >> Triangle >> Congruent Triangles >>

Define Congruent Triangles

Rules of Congruent Triangles Corresponding Parts of Congruent Triangles

Before you study this topic; you are advice to study

Define Congruent / Congruence
Congruence of Line Segment
Congruence of Angles

Congruent means "Equal in all respects"

Figures are said to be congruent whose shapes and sizes are both similar.

Two triangles are said to congruent when both are the exact copies of each another

Or we can also that:

Two triangles are said to congruent both cover each other exactly when superimposed.

And in other words, we can also say that:

When the corresponding parts of two triangles are equal or same, then triangles are said to be congruent.

The reverse of the above statement also holds true:
“When two triangles are congruent, then their corresponding parts are also equal or same”.

Example 1: Below are two triangles: △ ABC and △ PQR:

△ ABC is as follows:



△ PQR is as follows:



Now let’s place both angles over each another and observe what happens:



We can see that both the angles coincide over each other exactly.

we can also see that:

Corresponding Angles of both Triangles are equal i.e.:
∠ BAC = ∠ QPR, ∠ ACB = ∠ PRQ , ∠ CBA = ∠ RQP

Corresponding Vertices of both Triangles are equal i.e.:
A = P, C = R ,B = Q

Corresponding Lines of both Triangles are equal i.e.:
AC = PR, AB = PQ, BC = QR

Hence, we can say △ ABC and △ PQR are congruent

Or we can also write it as
△ ABC ≅ △ PQR:

Note: Order of letters in symbolic form of congruent triangle should display corresponding relationships. This means that the above symbolic representation of congruent triangles cannot be as:
∆ ABC ≅ ∆ QPR
Or ∆ ABC ≅ ∆ RPQ
Or ∆ BAC ≅ ∆ PQR
Or…………




Example 2: Below are two triangles: △ XYZ and △ RST:

△ XYZ is as follows:



△ RST is as follows:



Now let’s place both angles over each another and observe what happens:



We can see that both the △ XYZ and △ RST does not coincide over each other and corresponding angles, corresponding sides & corresponding vertical are also not equal.

Hence, we can say line segment △ XYZ and △ RST are not congruent

Or we can also write it as
△ XYZ ≇ △ RSTs


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