Congruent Triangles - SSS TestDate: 11/16/98 at 10:38:07 From: Doug Subject: SSS Geometry Can you explain SSS to me? Date: 11/16/98 at 11:04:37 From: Doctor Santu Subject: Re: SSS Geometry Yes, Doug! Suppose you have two different triangles, ABC and PQR. The question is: are they exactly the same size and shape? That's what we mean by "congruent." A triangle has 6 parts: 3 sides, and 3 angles. If two triangles are congruent, all six parts of one triangle will match all six corresponding parts of the other. There are tests we can do to check whether two triangles are congruent, and one of them is the SSS test. If three sides of one triangle are the same lengths as three sides of the other triangle, then they have to be congruent. (This is useful, because you only need to check three things, and you know that the other three parts will match up automatically. The name of the test, SSS, stands for "side-side-side". There's another one called the SAS test, for Side-Angle-Side.) Suppose in triangle ABC, AB = 12, BC = 15, and AC = 9. Suppose in triangle PQR, PQ = 9, QR = 15, and PR = 12. What would you say: are they congruent according to the SSS test? Yes, they are. Even though the order is different, the sides do match up, so we say that ABC is congruent to PRQ. (You have to name them so that corresponding angles match up. I'm not sure whether your teacher is picky about the difference between triangle PQR and triangle PRQ; I am!) Sometimes triangles are NOT congruent; for example, if one triangle has sides 2, 3 and 4, and the other triangle has sides 3, 4, 4, they're not congruent. Two sides match up, but the other side doesn't. Write back if you need a more detailed answer. - Doctor Santu, The Math Forum http://mathforum.org/dr.math/ |
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