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SSS Postulate 9699 Views


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Description:

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…

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Transcript

00:04

SSS Postulate, a la Shmoop.

00:09

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

00:12

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

00:15

They are always trying to outdo each other.

00:17

When Mr. Purple had his old BMW fixed,

00:19

Mrs. Yellow bought a shiny new one.

00:22

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

00:27

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

00:32

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

00:37

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

00:41

The only question was… whose lawn was bigger?

00:45

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

00:49

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

00:54

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

00:59

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

01:04

measures are exactly equal.

01:06

Basically, the triangles are identical to each other.

01:09

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

01:15

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

01:20

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

01:25

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

01:29

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

01:37

It's when something equals itself.

01:42

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

01:46

angle measures are congruent.

01:48

But triangles are special. Really special.

01:51

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

01:57

or SSS Postulate.

02:03

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

02:08

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

02:13

Basically, with SSS, we don't need to worry about angle measures.

02:17

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

02:21

with absolute certainty that the triangles themselves are congruent.

02:26

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

02:31

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

02:36

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

02:43

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

02:47

Guess who doesn’t exactly believe in ties?

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