Similarity and congruency

Similarity
1. Similar figures have the same shape but can be different sizes
  1. It can either be an enlargement or reduction
2. Two polygons are similar if:
  1. Their corresponding angles are equal (matching angles)
  2. Their corresponding sides are in the same proportion
3. The symbol for similar is |||
4. If two triangles have equal corresponding angles, their corresponding sides are in proportion
5. If two triangles have corresponding sides in proportion, corresponding angles are equal
6. You have to put the triangle in the order that it corresponds with the other triangle to find out whether it is similar
Congruency
1. To prove congruency compare, sides and anlges.
2. Congruent means identical and equal in all respects (2 triangles must be compared)
3. There are 4 cases of congruency
  1. 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)
    1. 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)
      1. 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
4. The symbol for congruency ->

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Similarity and congruency

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