CONGRUENT TRIANGLE

 


CONGRUENT TRIANGLE


CONGRUENT FIGURES: 
                                   
                      Congruent figures are exactly the same in size and shapes. In other words, shapes are congruent if one fits exactly over the other.

EXAMPLE:


CONGRUENT TRIANGLE:





Determining congruence

Sufficient evidence for congruence between two triangles in Euclidean space can be shown through the following comparisons:

  • SAS (side-angle-side): If two pairs of sides of two triangles are equal in length, and the included angles are equal in measurement, then the triangles are congruent.
  • SSS (side-side-side): If three pairs of sides of two triangles are equal in length, then the triangles are congruent.
  • ASA (angle-side-angle): If two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.

The ASA postulate was contributed by Thales of Miletus (Greek). In most systems of axioms, the three criteria – SAS, SSS and ASA – are established as theorems. In the School Mathematics Study Group system SAS is taken as one (#15) of 22 postulates.

  • AAS (angle-angle-side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent. AAS is equivalent to an ASA condition, by the fact that if any two angles are given, so is the third angle, since their sum should be 180°. ASA and AAS are sometimes combined into a single condition, AAcorrS – any two angles and a corresponding side.[3]
  • RHS (right-angle-hypotenuse-side), also known as HL (hypotenuse-leg): If two right-angled triangles have their hypotenuses equal in length, and a pair of shorter sides are equal in length, then the triangles are congruent.

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