If two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.[br][br][b][color=#0000ff]This is an extension of ASA. In ASA, since you know two sets of angles are congruent, you automatically know the third sets are also congruent since the sum of the interior angles are 180º in each triangle.[/color][/b][br][br]The "non-included" side in AAS can be either of the two sides that are not directly between the two angles being used.[br][br]Below is an example how to construct this. If you change anything in the construction, just click on the arrows on the top right to restore the construction.

[b][center][color=#ff0000]Now you try to draw a triangle congruent to the previous one[br][/color][br][color=#38761d]You need to draw a triangle with side AB=8cm an angle CAB of 40 degrees and angle BCA of 110 degrees. Try to do this in the "Applet" below[/color][/center][br][/b] [br][list=1][*]Use [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_segmentfixed.png[/icon] to draw segment AB and if you are requested to give the length type in 5[/*][*]Use  [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_anglefixed.png[/icon] to draw an angle at point A. ([color=#0000ff][b]Hint: Always click last on the point where you want the angle.[/b][/color]) If requested for the angle size type in 40 degrees. Lastly you need to select clockwise or counterclockwise. The direction of movement is from the line in a clockwise or counterclockwise direction.[/*][*]Use [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_ray.png[/icon] to draw a ray from point A through point B' that were created by the angle tool.[/*][*][color=#0000ff][b]The problem is you cannot draw the next angle as you do not know the length of side AC. But you do know that the sum of the interior angles of a triangle is 180 degrees. This imply that angle ABC=180-(40+110). Now I can construct an angle at point B.[/b][/color][/*][*]Use  [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_anglefixed.png[/icon] to draw an angle at point B. If requested for the angle size type in 30 degrees.[/*][*]Use [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_ray.png[/icon] to draw a ray from point B through point A' that were created by the angle tool.[/*][*]Use [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_intersect.png[/icon] to place point C at the intersection of the two rays[br][/*][*]Use [icon]https://tube.geogebra.org/images/ggb/toolbar/mode_polygon.png[/icon] to draw triangle ABC[br][/*][/list]

This is the same as for ASA. (See previous lesson)