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Congruence of Different Types of Triangles, Quadrilaterals and Circles

Any two objects are said to be congruent to each other, if they have same shape and size.

Let us discuss the congruency of few geometrical figures like triangles, quadrilaterals and circles.

Congruence of triangles

Consider the following triangles.

What do you observe in these triangles?

Here, ΔABC and ΔDEF are of the same shape and same size, which means these are congruent. However, the shape of ΔGHI is different from the remaining three, while the size of ΔJKL is different from the rest. Thus, there is no other pair of congruent triangles.

Now, observe the following scalene triangles.

These triangles are congruent by the correspondence PQR ↔ XYZ. This correspondence represents the following information:

∠P ≅ ∠X, ∠Q ≅ ∠Y, ∠R ≅ ∠Z and side PQ ≅ side XY, side QR ≅ side YZ, side PR ≅ side XZ

Congruency of these triangles, according to their correspondence, can be represented as ΔPQR ≅ ΔXYZ. It can be read as ‘Triangle PQR is congruent with triangle XYZ’.

Here, we cannot apply any other correspondence, such as P ↔ Y, Q ↔ Z, R ↔ X, etc. for the tria‚Ķ

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