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Centers of a Triangle 573 Views


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Description:

You might not think that the properties of a triangle would be particularly helpful in the realm of Tootsie Pop lickology. But boy, would you be wrong.

Language:
English Language
Common Core Standards:

Transcript

00:03

roving triangles congruent a la shmoop and now it's time for are your cats dear [Shmoop game show setting]

00:11

symmetrical first up we have this calico that was sent to us from a viewer in

00:18

Boston are these ears symmetrical you tell them the cat's ears are symmetrical [picture of cat]

00:24

we must first find if they are congruent in shape this cat's ears are in the

00:29

shape of isosceles triangle two sides of each are equal which means that the

00:35

angles opposite two equal sides are also equal this assertion is known as yes the

00:42

isosceles triangle theorem we can conclude that if two triangles are known

00:46

to be isosceles they are congruent if the corresponding side and a

00:51

corresponding angle are known to be congruent an extension of

00:55

angle-angle-side and yes we have confirmed that this cat's ears are

01:00

indeed symmetrical next we have this Persian specifically [people applauding]

01:06

bred to be perfectly symmetrical now this cat's ears are equilateral but

01:11

are they symmetrical check if this cat's ears are really equilateral we'd have to

01:17

see if they fulfill the theorem that every equilateral triangle is also

01:21

equipped angular each angle equaling 60 degrees F seems in order

01:28

the only other thing we really need to know is if this cat's ears are both the

01:32

same size it seems the left ear has sides that measure 5 centimeters in the [image of triangle]

01:37

right hand sides that measure 5 and 1/2 centimeters oh what a shame oh well next

01:43

catch will you look at this gorgeous Abyssinian we have here well folks it

01:49

appears we have a right angle alert this cat's ears form perfect right angles a

01:54

very rare occurrence on this show indeed you check for congruence there are

01:58

several theorems we can use the leg acute angle theorem based on angle side

02:03

angle the hypotenuse acute angle theorem based on angle angle side and of course

02:08

the hypotenuse leg theorem we've got congruent hypotenuse and we've got

02:13

congruent corresponding legs the ears are officially [cat on game show]

02:18

and now our last cat before we have to wrap up this segment a very special pair

02:24

of Siamese twins Siamese cats whose ears overlap this is the general shape of the

02:30

cat's ears as they overlap their owner apparently wants to know if they're

02:34

congruent to each other even though they've morphed together he tells us

02:39

that sides a B and a C as labeled in this carefully drawn representative

02:43

diagram are congruent as our a D and a e the triangles share a base and by the

02:50

axis Alize triangle theorem the angles often than those congruent sides are

02:54

also congruent so by side-angle-side these errors are congruent making these

02:59

cats Siamese identical twins well that's all the time we have this week thanks [twin cats on game show]

03:06

for watching our your cat's ears symmetrical and remember if they are

03:10

symmetrical your cat is defective good night

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