# Right-angle-Hypotenuse-Side

- Author:
- Herholdt Bezuidenhout

- Topic:
- Congruence, Right Triangles

## RHS Illustrated

## RHS Explained

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.
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:

**We can always use the Pythagorean Theorem to work out the third side and the use the SSS-Approach to construct this.****But, t****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)**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.## Example: Constructing RHS

## Steps in Constructing RHS

Now you try to draw a triangle congruent to the previous one You need to draw a triangle with side AB=8cm, right angle CAB and hypotenuse of 10cm. Try to do this in the "Applet" below

- Use to draw segment AB and if you are requested to give the length type in 8
- Use to draw a circle at point B and if requested to enter a radius type in 10
- Use to draw a line perpendicular to line AB through point A. (Click on line AB and then point A.)
- Use to place point C at the intersection of the perpendicular line and the circle
- Use to draw triangle ABC