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This postulate helps us compare congruent triangles. We'll get to Einstein's postulates regarding special relativity and inertial frames of reference next week. Or, um, maybe in three years or so…
|Geometry||Prove theorems involving similarity|
|Similarity, Right Triangles, and Trigonometry||Prove theorems involving similarity|
Mrs. Yellow bought a shiny new one.
When Mrs. Yellow put up lights and animatronic lawn ornaments for Christmas last year…
…Mr. Purple put a giant inflatable Santa on his lawn and gave out free candy canes to all the kids
Most recently, Mr. Purple had his front lawn redesigned into the shape of a triangle…
…and it was no surprise to him that two months later, Mrs. Yellow did the same.
The only question was… whose lawn was bigger?
If the two triangular lawns look like this, whose lawn is larger:
Mr. Purple's or Mrs. Yellow's?
To settle this dispute, we can find out whether or not the triangular lawns are congruent.
Remember if two triangles are congruent, that means all their side lengths and all their angle
measures are exactly equal.
Basically, the triangles are identical to each other.
In this case, our two triangles both have sides of lengths 6 feet, 8 feet, and 10 feet.
We know that when two sides are equal in length, they're congruent.
So the 6-foot sides are congruent to each other, the 8-foot sides are congruent to each other...
…and there's only one 10-foot side, which is congruent to itself, obviously.
If you're curious about the geometric way to say this, it's called Reflexive Property.
It's when something equals itself.
To prove that two shapes are congruent, we need to make sure all the side lengths and
angle measures are congruent.
But triangles are special. Really special.
Instead of finding all the angle measures, we can use a shortcut called Side-Side-Side,
or SSS Postulate.
The Side-Side-Side Postulate says that if all three sides of one triangle are congruent
to all three sides of another triangle, both these triangles are congruent.
Basically, with SSS, we don't need to worry about angle measures.
As long as we can prove that all three sides of both triangles are congruent, we can say
with absolute certainty that the triangles themselves are congruent.
Since we know the sides of Mr. Purple's lawn are 6 feet, 8 feet, and 10 feet in length…
and the sides of Mrs. Yellow's lawn are 6 feet, 8 feet, and 10 feet in length…
…we can say that, according to the SSS Postulate, the two triangles are congruent to each other.
So Mrs. Yellow's lawn and Mr. Purple's lawn are the exact same size.
Guess who doesn’t exactly believe in ties?