Similarity and congruency

Similarity and congruency

1. Similarity

   • Similar figures have the same shape but can be different sizes
     • It can either be an enlargement or reduction
   • Two polygons are similar if:
     • Their corresponding angles are equal (matching angles)
     • Their corresponding sides are in the same proportion
   • The symbol for similar is |||
   • If two triangles have equal corresponding angles, their corresponding sides are in proportion
   • If two triangles have corresponding sides in proportion, corresponding angles are equal
   • You have to put the triangle in the order that it corresponds with the other triangle to find out whether it is similar

2. Congruency

   • To prove congruency compare, sides and anlges.
   • Congruent means identical and equal in all respects (2 triangles must be compared)
   • There are 4 cases of congruency
     • 1. If three sides of a triangle are respectively equal to the three sides of the other triangle then the two triangles are congruent (SSS)
       • 2. If two sides and included angle of a triangle is respectively equal to the two sides and the included angle of another triangle ten they are congruent (SAS)
         • 3.If two angles and one side of one triangle are respectively equal to two angles and the corresponding side of another triangle, they are congruent (AAS or ASA)
           • 4.If the hypotenuse and one side of a right-angled triangle are respectively equal to the hypotenuse and one side of another right-angled triangle, they are congruent (RHS)
             • RHS - Right-angle, hypotenuse & side
   • The symbol for congruency ->

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