Similar Triangles Geometry Sources Discovering Geometry 2008 by
Similar Triangles Geometry Sources: Discovering Geometry (2008) by Michael Serra Geometry (2007) by Ron Larson
Similarity We define similar triangles in Geometry as triangles having the same shape; specifically having congruent corresponding angles and proportional corresponding sides.
Are the two triangles similar? 5 7 6 15 21 Yes they are! Scale factor is 3! Because the triangles are similar, the corresponding angles are congruent! 18
Similar Triangles AA Similarity Postulate If two angles of a triangle are congruent to two angles of another triangle, then the two triangles are similar.
AA Similarity Are the two triangles similar ?
AA Similarity Are the two triangles similar ?
Similar Triangles SSS Similarity Conjecture If the ratios of the 3 pairs of corresponding sides of two triangles are equal, then the two triangles are similar.
SSS Similarity Are the two triangles similar ? All 3 pairs of sides have equal ratios! Therefore the two triangles are similar!
Similar Triangles SAS Similarity Conjecture If the ratios of 2 pairs of corresponding sides of two triangles are equal, and the included angles are congruent, then the two triangles are similar.
SAS Similarity Are the two triangles similar ? Yes they are similar by SAS Similarity Conj.
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