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SSS and SAS - Problem 1

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

One way of finding out if two triangles are congruent is if all three sides of both triangles are congruent. You can tell if sides of a triangle are congruent if they have the same number of dashes running through them. If for each side of a triangle, there is a corresponding side that is congruent in the other triangle, the two triangles are congruent.

It is important to label the triangles in such a way that they are congruent. For example, triangle ABC being congruent to triangle DEF implies that AB is congruent to DE, BC is congruent to EF, and CA is congruent to FD.

Let’s look at these two triangles first we’re going to ask can we say that two triangles are congruent and then we’ll say well which short cut are we using. Well we see AC corresponds to EF, we see that AB corresponds to DE and we see that CB corresponds to DF.

So we know three corresponding sides are congruent, so I’m going to say that triangle ABC is congruent to this triangle DEF. But what’s the order that I’m going write my vertices at? It has to be very specific. Angle A has top correspond to a certain angle in this triangle.

Let’s start by looking at side AB. Side AB has one mark which means that it must be congruent top DE, so I’m going to write DE first, which means that AB corresponds to DE. Well that makes it pretty easy because there’s only one other vertex and that’s F. So triangle ABC is congruent to triangle DEF and our short-cut is side-side-side.

So you notice what we did, by only knowing the three sides of this two triangles we are able to say that everything about them must be congruent.

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