How to Tell If Triangles Are Congruent

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Congruence is an important concept when you are dealing with triangles. For example, if you have a box with ends that are triangular, the two end pieces will need to be congruent triangles. Congruent simply means the same size and shape. Fortunately, there are rules that govern triangles, and these rules make it pretty easy to find out if a triangle is congruent. Read on to learn how to tell if triangles are congruent.

Measure All Three Sides

The SSS Theorem, or Side Side Side Theorem, says that if two triangles have three sides with the same length, they are congruent. If the three sides are congruent, then the angles will be congruent, and the triangles will be the same shape and the same size. This theorem is true all the time, even if the triangles are mirror images when you look at them. If you can measure the sides, you will find out if the triangles are congruent.

Measure the Angles and Sides

There are other theorems that prove that triangles are congruent. For example, the SAS (Side Angle Side) Theorem says that if two sides and the angle between them have the same measure on each triangle, then the triangles are congruent. In addition, the ASA (angle side angle) theorem says that if you know the measure of two angles and the side between them and they are the same, then the triangles are congruent. This also works with the AAS (angle angle side) theorem, when you know two angles and the side that is not included. In any of these scenarios, if the measures are the same, then the two triangles are congruent.

Measure the Hypotenuse and One Leg of a Right Triangle

Right triangles have what is called a hypotenuse, which is the side that is opposite the right angle. A right angle is 90 degrees. If you measure the hypotenuse and one of the legs, and you find that they are the same, then the triangles are congruent.

It is important to note that if you only know the measures of the three angles, and they are the same, the triangles are not necessarily congruent. They might be similar, meaning that they are in proportion to each other, but having the same angle does not mean they are the same shape and the same size.

The key is to remember that you always need to know the measure of at least one side of the triangles to determine whether they are congruent. Congruent triangles will have all three sides and all three angles be exactly the same. If you place one on top of the other, they will be identical. It is very important to know whether triangles are congruent when you are constructing anything that uses angles in the real world, because if they are not, your entire design could fail.

Geometry is a precise subject, and it is not hard to master if you know the rules. The rules above make it very easy to determine whether or not triangles are congruent. There is additional information that might help. The three angles in a triangle will always add up to 180 degrees. For this reason, if you know two angles, you can find out what the measure of the third angle is. If two triangles have three equivalent angles, they are similar, but you will need to know the length of at least one side to determine if they are congruent.

Right triangles are unique because one angle always measures 90 degrees. The other two angles added together will equal 90 degrees as well. No matter what information is given, you will always know the 90 degree angle. This will be one less angle to measure or calculate. If you want to know whether triangles are congruent, you just need to know the theorems listed above.

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