Similarity is when two or more geometric shapes are of the same shape. These shapes are said to be similar. Similar shapes are identical in all senses except size.

Proving Triangles are Similar

There are many ways of proving that two triangles are similar. The ways of proving the similarity of two triangles are the following:

  1. AA or Angle-Angle. If two angles of each triangle are congruent, then the two triangles are similar.
  2. SSS or Side-Side-Side. If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
  3. SAS or Side-Angle-Side. If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.
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