Mathematics Class VII

Integers
Fractions and Decimals
Exponents and Powers
Algebraic Equations
Simple Linear Equations
Lines and Angles
Comparing Quantities
Congruence of Triangles
Rational Numbers
Perimeter and Area
Data Handling
Practical Geometry
Symmetry
Visualising Solid Shapes

Congruence Of Triangles

If we superpose one triangle over other triangle and they cover each other properly, then they must be congruent triangles.

In case of congruent triangles-

• All the sides of one triangle must be equal to the corresponding sides of another triangle.
• All the angles of one triangle must be equal to the corresponding angles of another triangle.
• All the vertices of one triangle must be corresponding to the vertices of another triangle.

In the above triangles,

If, ∆ABC ≅ ∆FDE then

• Corresponding vertices are – ∠A ↔ ∠F, ∠B ↔ ∠D and ∠C ↔ ∠E
• Corresponding angles are – ∠A ↔ ∠F, ∠B ↔ ∠D and ∠C ↔ ∠E
• Corresponding sides are – AB ↔ FD, BC ↔ DE and AC ↔ FE

Remark: It is the order of the letters in the names of congruent triangles which tells the corresponding relationships between two triangles. If we change it from ∆ABC ≅ ∆FDE to ∆BCA ≅ ∆FDE, then it is not necessary that the two triangles are congruent as it is important that all the corresponding sides, angles and vertices are same.

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