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SSS Postulate, a la Shmoop.

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Ever since Mr. Purple and Mrs. Yellow became next-door neighbors,

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they've had a little rivalry going on between them.

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They are always trying to outdo each other.

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When Mr. Purple had his old BMW fixed,

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Mrs. Yellow bought a shiny new one.

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When Mrs. Yellow put up lights and animatronic lawn ornaments for Christmas last year…

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…Mr. Purple put a giant inflatable Santa on his lawn and gave out free candy canes to all the kids

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Most recently, Mr. Purple had his front lawn redesigned into the shape of a triangle…

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…and it was no surprise to him that two months later, Mrs. Yellow did the same.

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The only question was… whose lawn was bigger?

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If the two triangular lawns look like this, whose lawn is larger:

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Mr. Purple's or Mrs. Yellow's?

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To settle this dispute, we can find out whether or not the triangular lawns are congruent.

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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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Basically, the triangles are identical to each other.

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In this case, our two triangles both have sides of lengths 6 feet, 8 feet, and 10 feet.

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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 other...

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…and there's only one 10-foot side, which is congruent to itself, obviously.

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If you're curious about the geometric way to say this, it's called Reflexive Property.

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It's when something equals itself.

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To prove that two shapes are congruent, we need to make sure all the side lengths and

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angle measures are congruent.

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But triangles are special. Really special.

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Instead of finding all the angle measures, we can use a shortcut called Side-Side-Side,

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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.

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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…

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and the sides of Mrs. Yellow's lawn are 6 feet, 8 feet, and 10 feet in length…

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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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So Mrs. Yellow's lawn and Mr. Purple's lawn are the exact same size.

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Guess who doesn’t exactly believe in ties?

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