Difference between revisions of "AA similarity"
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In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar. | In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar. | ||
| − | Proof | + | ==Proof== |
Let ABC and DEF be two triangles such that <math>\angle A = \angle D</math> and <math>\angle B = \angle E</math>. | Let ABC and DEF be two triangles such that <math>\angle A = \angle D</math> and <math>\angle B = \angle E</math>. | ||
<math>\angle A + \angle B + \angle C = 180</math> and | <math>\angle A + \angle B + \angle C = 180</math> and | ||
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\angle D + \angle E + \angle C = \angle D + \angle E + \angle F</math>, since we know that <math>\angle A = \angle D</math> and <math>\angle B = \angle E</math>, from before. | \angle D + \angle E + \angle C = \angle D + \angle E + \angle F</math>, since we know that <math>\angle A = \angle D</math> and <math>\angle B = \angle E</math>, from before. | ||
Therefore, by subtracting <math>\angle D + \angle E</math> by both equations, we get <math>\angle C = \angle F</math>. | Therefore, by subtracting <math>\angle D + \angle E</math> by both equations, we get <math>\angle C = \angle F</math>. | ||
| + | |||
| + | ==See also== | ||
| + | * [[Similarity (geometry)]] | ||
| + | * [[SAS similarity]] | ||
| + | * [[SSS similarity]] | ||
Revision as of 00:52, 19 December 2020
Theorem: In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.
Proof
Let ABC and DEF be two triangles such that 
and 
.
and
Thus, we can write the equation: 
, since we know that and , from before.
Therefore, by subtracting 
by both equations, we get 
.
