Understanding Congruence in Mathematics | Definition, Examples, and Applications

congruent

In mathematics, congruent refers to two shapes or figures that have the same size and shape

In mathematics, congruent refers to two shapes or figures that have the same size and shape. When two figures are congruent, it means that all corresponding sides are equal in length, and all corresponding angles are equal in measure.

Congruence can be used to compare and classify various geometrical figures. For example, two triangles are congruent if all three pairs of corresponding sides are equal in length and all three corresponding angles are equal. Congruent triangles can have different orientations or positions, but they will have the same shape and size.

When we say that two shapes are congruent, it implies that we can superimpose one shape onto the other perfectly, without any overlap or gaps. We can think of it as if they are exactly the same, just in different positions or orientations.

Congruence can be represented using different notations. For lines, we use “≡” symbol to show that two segments or lines are congruent. For angles, we use the symbol “≅” to represent congruence. For example, if we have two line segments AB and CD, and they have the same length, we can write it as AB ≡ CD. Similarly, if we have two angles ∠ABC and ∠DEF, and they have the same measure, we can express it as ∠ABC ≅ ∠DEF.

Overall, congruence is an important concept in geometry as it helps us to determine the equality of shapes and figures, allowing us to make comparisons and solve various geometric problems.

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