Difference between revisions of "AA similarity"
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==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 | + | The sum interior angles of a triangle is equal to 180. <math>\angle A + \angle B + \angle C = 180</math> and |
<math>\angle D + \angle E + \angle F = 180</math> | <math>\angle D + \angle E + \angle F = 180</math> | ||
Thus, we can write the equation: <math>\angle A + \angle B + \angle C=\angle D + \angle E + \angle F \Longrightarrow | Thus, we can write the equation: <math>\angle A + \angle B + \angle C=\angle D + \angle E + \angle F \Longrightarrow | ||
Revision as of 00:15, 24 December 2022
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 
.
The sum interior angles of a triangle is equal to 180. 
and
Thus, we can write the equation: 
, since we know that and , from before.
Therefore, by subtracting 
by both equations, we get 
.
See also
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