Which triangles are congruent? Henning Hraban Ramm / Pixelio

### Congruent triangles - you need to know

In this topic old school knowledge needs to be refreshed. For congruent triangles - these are congruent triangles.

- Congruent means that you can superimpose two or more triangles and these are then made to coincide, so match in all sides and angles.
- Such triangles can not distinguish further in principle, they are not identical twins dissimilar.
- The technical term for congruent way congruent. Congruent triangles are therefore congruent.

### Congruent triangles - so you recognize them

- If you should decide whether two - for example, on paper or in a coordinate system specified triangles - are congruent and congruent, it is of course the easiest to cut one of the two triangles and place on the other. Does it - under your cutting accuracy - one above the other without protruding surface? Then the two triangles are congruent.
- But what if you can not cut the paper (or want)? For this problem, there are solutions, namely geometrical figures which convert a character to another.
- These figures include translations, rotations, and flipping. If you make it through such an image (or more in a row), the map a triangle on the other, the two triangles are congruent or congruent. Most the judgment already gives this a good indication.

### Congruence - as they are applied

Sometimes you have but, perhaps in a more complex geometric figure or a proof already contain information on two triangles to be congruent. Maybe you know the side lengths or certain angle. It is important that you always need three determining factors. In this case, help the four congruence that apply to congruent triangles:

- The first is simple and easy to understand: If you have two triangles that match in all three pages, these two triangles are congruent. Abbreviated name of this congruence sss (the "s" stands for page).
- The second congruence reveals itself vividly: If your two triangles coincide in two pages and the angle therebetween, they are congruent. In fact, this construction does not allow more freedom for several triangles. Try it out. Abbreviated reads the sentence PBUH (where "w" stands for angle).
- At the third set of a page is sufficient, but two angles which bear this page. Again, can be constructed only a triangle. formulated Short's wsw this sentence.
- The fourth congruence is a bit more difficult to understand, because he has sort of a secondary condition: the to be examined by you triangles are congruent then, if you agree on two sides and an angle. However, the angle of the larger of the two sides must be opposite this time. Even when drawing a triangle reveals that in fact two different triangles arise when the angle of the smaller sides facing. As shorthand to remember for this set Sw. The big "S" is intended to indicate the constraint with the larger side.