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SSS Postulate, a la Shmoop Ever since Mr. Purple and Mrs. Yellow [Mr Purple and Mrs Yellow walk out their houses]

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became next-door neighbors, they've had a little rivalry going on between them. [They shout at each other]

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When Mr. Purple had his old BMW fixed ,Mrs. Yellow bought a shiny new one. [Mr Purple in his old BMW, Mrs Yellow in her new BMW]

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When Mrs. Yellow put up lights for Christmas last year… [Christmas lights on Mrs Yellows house]

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…Mr. Purple put a giant inflatable Santa on his lawn. [Giant Santa inflating]

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Most recently, Mr. Purple had his front lawn redesigned into the shape of a triangle… [Mr Purple on a ride-on lawnmower]

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…and it was no surprise to him that Mrs. Yellow did the same. [Mrs Yellow cutting her lawn into a triangle]

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The only question was…

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whose lawn was bigger?

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To settle this dispute we can find out whether or not the triangular lawns are congruent. [Mr Purple and Mrs Yellow pointing at each other]

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Remember if two triangles are congruent, that means all their side lengths and all their angle

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measures are exactly equal.

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In this case, our two triangles both have sides of lengths 6 feet, 8 feet, and 10 feet. [The two traingles drawn next to each other]

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We know that when two sides are equal in length, they're congruent.

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So the 6-foot sides are congruent to each other, the 8-foot sides are congruent to each

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other…

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…and there's only one 10-foot side, which is congruent to itself. [Arrows pointing to the different lengths]

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To prove that two shapes are congruent, we need to make sure all the side lengths and [Teacher at the front of a class]

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angle measures are congruent.

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But triangles are special.

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Instead of finding all the angle measures, we can use a shortcut called Side-Side-Side, [Classroom full of students]

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or SSS Postulate.

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The Side-Side-Side Postulate says that if all three sides of one triangle are congruent

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to all three sides of another triangle, both these triangles are congruent.

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Basically, with SSS, we don't need to worry about angle measures. [Two snakes in love]

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As long as we can prove that all three sides of both triangles are congruent, we can say

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with absolute certainty that the triangles themselves are congruent.

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Since we know the sides of Mr. Purple's lawn are 6 feet, 8 feet, and 10 feet in length… [Mr Purple mowing his lawn]

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and the sides of Mrs. Purplethorn's lawn are 6 feet, 8 feet, and 10 feet in length… [Mrs Yellow mowing her lawn]

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…we can say that, according to the SSS Postulate, the two triangles are congruent to each other.

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And are the exact same size.

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Guess who doesn’t exactly believe in ties? [Mr Purple and Mrs Yellow running at each other with shovels]

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