Similarity and Congruency

Similarity and Congruency

1. Gongruency

   • Conditions
     • SSS(Side-Side-Side)
       • Definition: Triangles are congruent if all three sides in one triangle are congruent to the corresponding sides in the other.
       • In the figure on the above, the two triangles have all three corresponding sides equal in length and so are still congruent, even though one is the mirror image of the other and rotated.
     • SAS(Side-Angle-Side)
       • Definition: Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles.
     • ASA(Angle-Side-Angle)
       • Definition: Triangles are congruent if any two angles and their included side are equal in both triangles
     • RHS(Right angle-Hypotenuse-Side)
       • Definition: Two right angled triangles are congruent if the hypotenuse( longest part of a right angled triangle) and the same length for one of the sides
   • Definition: Triangles are congruent when all corresponding sides and interior angles are congruent. The triangles have the same shape and size, but one may be a mirror image of the other or how you rotate or move it around

2. Similarity

   • Conditions
     • SSS(Side-Side-Side)
       • Definition: Triangles are similar if all three sides in one triangle are in the same proportion to the corresponding sides in the other.
     • SAS(Side-Angle-Side)
       • Definition: Triangles are similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are equal
     • AA(Angle-Angle)
       • Definition: Triangles are similar if the measure of all three interior angles in one triangle are the same as the corresponding angles in the other.
   • Definition: Triangles are similar if they have the same shape, but different sizes. (They are still similar even if one is rotated, or one is a mirror image of the other).

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