Aa similarity
![aa similarity aa similarity](http://eoffeducation.weebly.com/uploads/1/3/9/9/13997549/534821_orig.png)
Given: \(\angle A\) = \(\angle D\), \(\angle B\) = \(\angle E\) and \(\angle C\) = \(\angle F\). Triangle Similarity Test AAA All corresponding angles equal. \Ĭonsider the equi-angular triangles, \(\Delta ABC\) and \(\Delta DEF\) DB 2(2) + 1 CB 2 (2) ± 1 + 12 16:(5 GD, DH 62/87,21 We know that ( Reflexive Property) and are given Therefore, by AA Similarity. This means that their sides will also be proportional, that is: Use the corresponding side lengths to write a proportion. Using the AA criterion, we can say that these triangles are similar. Ideally, the name of this criterion should then be the AAA(Angle-Angle-Angle) criterion, but we call it as AA criterion because we need only two pairs of angles to be equal - the third pair will then automatically be equal by angle sum property of triangles.Ĭonsider the following figure, in which \(\Delta ABC\) and \(\Delta DEF\) are equi-angular,i.e.,
![aa similarity aa similarity](https://i0.wp.com/img.yumpu.com/31807017/1/500x640/geometry-10-4-inscribed-angles.jpg)
In short, equi-angular triangles are similar. The AA criterion for triangle similarity states that if the three angles of one triangle are respectively equal to the three angles of the other, then the two triangles will be similar. The AA criterion for triangle similarity states that if the three angles of one triangle are respectively equal to the three. and Thus, we can write the equation:, since we know that and, from before.
![aa similarity aa similarity](https://us-static.z-dn.net/files/d52/0ad569b73e21227742e7c4d0d382b5d6.png)
Let ABC and DEF be two triangles such that and. However, in order to be sure that two triangles are similar, we do not necessarily need to have information about all sides and all angles. Theorem: In two triangles, if two pairs of corresponding angles are congruent, then the triangles are similar.