ShmoopTube

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

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

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

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

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

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

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

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

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corresponding angle are known to be congruent an extension of

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

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

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

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

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

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equipped angular each angle equaling 60 degrees F seems in order

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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symmetrical your cat is defective good night

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