If the hypotenuse and one side of a right-angled triangle are congruent to the corresponding parts of another right triangle, the right-angled triangles are congruent.[br][br]Remember during SSS we also experience that the triangle became a right-angle triangle when the sides were Pythagorean Triples. Read more about Pythagorean Triples by clicking here:[br][br][list][*][url=http://www.mathsisfun.com/pythagorean_triples.html]Pythagorean Triples: Basics[/url][br][/*][/list][list][*][url=http://www.mathsisfun.com/numbers/pythagorean-triples.html]Pythagorean Triples: Advanced[/url][br][/*][/list][br][color=#0000ff][b]We can always use the Pythagorean Theorem to work out the third side and the use the SSS-Approach to construct this. [/b][/color][color=#ff0000][b]But, t[/b][/color][b][color=#ff0000]his is a special case of ASS that will be discussed in more detail under the section about problematic methods. (See the "Donkey Theorem" for more details)[/color][/b][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[/color][br][br][color=#38761d]You need to draw a triangle with side AB=8cm, right angle CAB and hypotenuse of 10cm. [br]Try to do this in the "Applet" below[/color][/center][/b][br] [br][list=1] [*]Use [icon]/images/ggb/toolbar/mode_segmentfixed.png[/icon] to draw segment AB and if you are requested to give the length type in 8[/*] [*]Use [icon]/images/ggb/toolbar/mode_circlepointradius.png[/icon] to draw a circle at point B and if requested to enter a radius type in 10[br][/*][*]Use [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon] to draw a line perpendicular to line AB through point A. (Click on line AB and then point A.)[/*] [*]Use [icon]/images/ggb/toolbar/mode_intersect.png[/icon] to place point C at the intersection of the perpendicular line and the circle[/*] [*]Use [icon]/images/ggb/toolbar/mode_polygon.png[/icon] to draw triangle ABC[/*][/list]