Difference between revisions of "AA similarity"
Megaboy6679 (talk | contribs) m |
|||
Line 4: | Line 4: | ||
==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 01:15, 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
This article is a stub. Help us out by expanding it.