In geometry two triangles are similar if the corresponding sides are in proportion. If two angles are the same, the are also similar. If two angles are the similar, in fact, all three angles must be the same.

For example

In triangle ABC, AB = 10, BC = 15, AC = 18

In triangle DEF, DE = 20, EF = 30, DF = 36

These triangles are similar because corresponding sides are in proportion

10/20 = 15/30 = 18/36. All three fractions simplify to 1/2

Try another example.

Triangle ABC, AB = 5, BC = 12, AC = 15

Triangle DEF, DE = 15, BC = 30, AC = 45

For the triangles to be similar, 5/15 = 12/30 = 15/45

Simplify each fraction to get 1/3 = 2/5 = 1/3.. Notice this is a false statement, so the triangles are not similar

Another example dealing with the angles

Triangle ABC, <A = 45, <B = 89

Triangle DEF, <E = 89, <F = 46

<C = 180 - (45 + 89) = 46

<D = 180 - (46 + 89) = 45

<A corresponds with <D, <B corresponds with <E and <C corresponds with <F. Since the angles are congruent, the triangles are similar.

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