![]() Rules for Angles in Parallel Lines are also used, in particular, the following Alternate Interior Angles Rule: In the next two examples, Congruent Triangles are found within the given Geometric Shapes, which allows side lengths to be proven as equal. The following video shows some more complex examples, where triangle sides are joined together to other triangles and shapes. The following examples show the required working out for demonstrating that a pair of Triangles are identical. This next one is a heavy metal Parody (sounds a bit like a Joan Jet song): ![]() Here is a quick little tune by Abbie about the Triangle Rules, mentioning exclusion of the invalid Angle Side Side “Donkey Rule”. There are four rules that we use to determine if Triangles are congruent: SSS, SAS, AAS, and RHS. The following video shows why there is not an SSA Rule for congruent triangles. Pythagoras Rule means that the missing side lengths have to be equal, so we are indirectly using the “SSS” Rule here. This Rule works because of Pythagoras Theorem for 90 Degree Triangles. The following “YayMath” 26 minute gives a comprehensive lesson on the ASA and AAS Rules.Īny two Right-Angled 90 degree Triangles are congruent if the hypotenuse and one pair of matching sides are equal in length. However, most people these days just use “AAS”, so that there is one less congruency rule to memorise. It is quite okay to use the “ASA” Rule if the order of the items is “ASA” as shown in the above diagram. There is also an old “ASA” Angle Side Angle Rule however this has been brought in to be part of the “AAS” Rule. Two triangles are congruent if two matching angles are equal and a matching side is equal in length. The American teacher doing the videos does not always use the most correct language, but he is enthusiastic and explains his examples well.ĪAS – Angle Angle Side Rule for Triangles The following video covers the “SSS” and “SAS” Rules for Congruent Triangles. The angle included by these sides is the same. ![]() Two Triangles will be congruent if two matching sides have equal lengths and Going A to B to C should be the exact same path as D to E to F. We need to make sure the order of the letters matches going around the two triangles in the same order of sides. We need to be careful with the labelling when our Triangles are in different positions.Įg. When we say the Triangles are Congruent using their letters, we need to make sure the order of the letters matches the path around the two triangles correctly. In addition, Triangles are usually labelled with capital alphabet letters. This triple ine symbol is what we use in Australia however some other countries use an equals sign with a squiggly “tilda” line added to the top of it. There is a special symbol we use to indicate that Triangles are Congruent, that is like an equals sign with an extra line added on top of it. Instead we have markers to show where the matching same length sides are on the two triangles.įor these Triangles we can apply the “SSS” rule, as long as we have all three sides matching each other on the two triangles. In diagrams, the actual values of the sides are sometimes not given. ![]() This is called “SSS” or the “Side Side Side Rule”. We can actually use just the three sides to work out if two triangles are congruent. The first of these “Shortcut Rules” is the “Side Side Side”, or “SSS” Rule. There are FOUR “Shortcut Rules” for Congruent Triangles that we will be covering in this lesson. It turns out that we do not have to check all the sides and angles of two Triangles to work out that they are Congruent. The following Video by Mr Bill Konst about Congruence, covers the “SSS Rule for Triangles”, as well as covering Quadrilaterals and some interesting optical illusions. The position of the matching Triangles does not affect the fact that they are identical, or “Congruent”. The Identical (eg.”Congruent”) Triangles can be in different positions, (or orientations), and still be the exact same size and shape. This means that the matching sides must be the same length and the matching angles must be the same size. Two triangles are congruent if they are completely identical. Here are a typical pair of Congruent Triangles Image Copyright 2013 by Passy’s World of Mathematics pairs of Triangles which have the exact same size and shape.Ĭongruent Triangles are an important part of our everyday world, especially for reinforcing many structures. This lesson is all about “Congruent Triangles”, eg. When two items have the exact same size and shape, we say that they are “Congruent”. Identical Twins have the exact same size and shape, and we instantly recognise that the two of them are exactly the same.
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