Similarity & Congruency
Properties of similar and congruent figures
Similarity and Congruency
Congruent figures have the same shape AND size. Similar figures have the same shape but may be different sizes (one is an enlargement of the other). For similar figures, corresponding angles are equal and corresponding sides are in proportion.
Example
Testing for Similarity
Triangle ABC: sides 3, 4, 5 cm; angles 37°, 53°, 90°
Triangle DEF: sides 6, 8, 10 cm; angles 37°, 53°, 90°
Ratios: 6/3 = 8/4 = 10/5 = 2
All ratios equal → triangles are similar (scale factor 2)
Conditions for Congruence (Triangles)
Triangles are congruent if:
• SSS: all three sides equal
• SAS: two sides and the included angle equal
• ASA: two angles and the included side equal
• RHS: right angle, hypotenuse and one side equal
Note
Remember
Similar = same shape (angles equal, sides proportional). Congruent = same shape AND size (all corresponding parts equal). Scale factor relates corresponding sides of similar figures.
Key Vocabulary
SimilarSame shape but not necessarily the same size
CongruentExactly the same shape and size
Scale factorThe ratio by which a shape is enlarged or reduced
ProportionCorresponding sides have equal ratios
CorrespondingIn the same relative position
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