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SAT Math 5.5 Geometry and Measurement 254 Views


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SAT Math 5.5 Geometry and Measurement

Language:
English Language

Transcript

00:03

Here’s your shmoop du jour, brought to you by triangles of all shapes and sizes.

00:08

Triangle ABC is similar to triangle EDC, which is also similar to triangle EFG.

00:14

Find the perimeter of triangle EFG.

00:16

Here are the potential answers...

00:20

They’ve gotten us off to a slow start… all we know is that side FG is “1.”

00:25

Now how do we find FE and EG?

00:29

What do we know about similar triangles?

00:32

All corresponding angles are equal from one to the next…okay, good to know…

00:36

…and the other thing is that all corresponding sides have a relative length.

00:40

In other words, if the length of one side is doubled, then the lengths of all sides are doubled.

00:48

Triangle ABC isn’t going to help us much at the moment…

00:51

…because although two of its sides are labeled, it’s missing the one that we do have for triangle EFG.

00:57

Whereas, with triangle EDC, the side that is labeled as “3” directly corresponds to side FG.

01:04

So now we know that everything in triangle EDC is triple that of triangle EFG.

01:09

We also know that line CE is 2.25…so if the corresponding side in triangle EFG, side

01:16

EG, is one-third of that length… it must be 0.75 units in length.

01:22

All right…now we can see the relationship between triangles EFG and ABC.

01:27

Looks like ABC is twice as large as its counterpart to the right.

01:32

In that case, since line AB is “2,” line EF must be “1.”

01:38

And now it’s just a case of adding ‘em up… 1 plus 1 plus 0.75 = 2.75…

01:45

…answer A.

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