Similar Triangles Examples
Definitions and theorems related to similar triangles are discussed using examples. Also Problems on similar triangles may be found in this site.
DefinitionTwo triangles ABC and A'B'C' are similar if the three angles of the first triangle are congruent to the corresponding three angles of the second triangle and the lengths of their corresponding sides are proportional as follows.
TheoremAngle-Angle (AA) SimilarityIf two angles in a triangle are congruent to the two corresponding angles in a second triangle, then the two triangles are similar.Example 1Let ABC be a triangle and A'C' a segment parallel to AC. What can you say about triangles ABC and A'BC'? Explain your answer.Solution to Example 1:
TheoremSide-Side-Side (SSS) SimilarityIf the three sides of a triangle are proportional to the corresponding sides of a second triangle, then the triangles are similar.Example 2Let the vertices of triangles ABC and PQR defined by the coordinates: A(-2,0), B(0,4), C(2,0), P(-1,1), Q(0,3), and R(1,1). Show that the two triangles are similar.Solution to Example 2
TheoremSide-Angle-Side (SAS) SimilarityIf an angle of a triangle is congruent to the corresponding angle of a second triangle, and the lengths of the two sides including the angle in one triangle are proportional to the lengths of the corresponding two sides in the second triangle, then the two triangles are similar.Example 3Show that triangles ABC and A'BC', in the figure below, are similar.Solution to Example 3:
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