Fix the mistake: Similarity and Scaling
Similarity and Enlargement/Reduction ① Rules of Similarity
When two figures have “the same shape but different sizes,” they are called “similar.” Let us learn the conditions under which two triangles are similar.
🔑 3 Conditions for Triangles to Be Similar
- The ratios of all three pairs of corresponding sides are equal (SSS similarity)
- The ratio of two pairs of corresponding sides is equal, and the included angles are equal (SAS similarity)
- Two pairs of corresponding angles are equal (AA similarity)
Example: There are triangles △ABC and △DEF. If ∠A = ∠D = 60° and ∠B = ∠E = 70°, are these two triangles similar? If they are similar, give the reason.
Solution:
① Since ∠A = ∠D and ∠B = ∠E, two pairs of corresponding angles are equal
② Therefore, they are AA similar
③ The remaining angles are also automatically determined: ∠C = ∠F = 50°
Solution:
① Since ∠A = ∠D and ∠B = ∠E, two pairs of corresponding angles are equal
② Therefore, they are AA similar
③ The remaining angles are also automatically determined: ∠C = ∠F = 50°
In problems involving parallel lines, it is often useful to show that “two pairs of angles are equal” using alternate interior angles or corresponding angles, and then conclude that the triangles are AA similar.
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