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SSS and SAS - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

When two triangles are congruent, all three pairs of corresponding sides are congruent and all three pairs of corresponding angles are congruent. If all three pairs of corresponding sides are congruent, the triangles are congruent. This congruence shortcut is known as side-side-side (SSS). Another shortcut is side-angle-side (SAS), where two pairs of sides and the angle between them are known to be congruent. SSS and SAS are important shortcuts to know when solving proofs.

If two triangles are congruent, if I say that triangle abc and triangle def are congruent then that means that all of their corresponding parts are also congruent which means a and d will be congruent angle b and angle e will be congruent, angle c and angle f will be congruent. And then we can talk about the sides, de will be congruent to ab, bc would be congruent to ef and df would be congruent to ac. So this is a whole work going on here there's 6 different parts of these two triangles that could be congruent. Do we always need to know that those 3 angles and those three sides are congruent? And the answer is no. There are a couple of shortcuts and we're going to talk about two.
The first is side side side. But what do side side side mean? It means if all you know is the 3 sides of one triangle are congruent and corresponding to the 3 sides of another triangle, then yes those two triangles must be congruent.
The second shortcut that we're going to talk about is side angle side. Side angle side means if you have a side and an included angle, which means if I said side de and side df the included angle would be angle d so it's the angle that's formed by those two sides then here you can also say those two [IB] triangles must be congruent.

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