ShmoopTube

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properties of equality and congruence a la shmoop

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here we see except that their horns twist and branch in various sharp angles [goats on mountain]

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usually farming polygons today wildlife researcher and go-to expert Sarah Nevada [goat's horns form polygons]

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intends to bust the local myth that no two mountain goats horns will ever grow [goats in a field]

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into the same shape aha it seems sarah has found three [three goats with triangle horns]

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candidates whose horns at first glance grow in about the same shape we'll call

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these goats a B and C let's get a close-up on those warrants how does

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Sarah determine if the shapes of the goats horns are identical or in

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geometric terms congruent goat A's horns grow in a triangle shape let's label the [woman on mountain top]

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points of the triangle X sub a y sub T and Z sub a from these measurements we [goat with triangle horns]

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can draw the definite conclusion the triangle X sub a y sub a Z sub a is

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congruent to triangle X of a y sub a Z sub a when a geometric element is equal

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to itself it's demonstrating the reflexive property of congruence now

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let's move on to goat B's horns which also grow in a triangle shape let's

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label the points X sub B Y sub P and Z sub P Sara's hoping that goat a and goat

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B's horns form the same triangle thereby refuting the myth if triangle a is [both goats together]

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congruent to triangle B we can conclude the triangle B is congruent to triangle

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a this demonstrates the symmetric property of congruence which illustrates

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that equality is a two-way street now triangle a is congruent to triangle [cars driving past each other]

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B we can look at goat C's likewise triangular horns and follow the same

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logic the triangle C is congruent to triangle B and we've previously

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established the triangle V is common - triangle a we can conclude the

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triangle C is also congruent to triangle a this series of equalities demonstrates

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the transitive property of congruence the geometric properties of equality and

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congruence are pretty intuitive but it's important to know that they exist

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unfortunately for Sarah the go-to expert she's just come across an undercoat or [goat chases Sarah]

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rather threatening for information' maybe she'll study gorilla [Sarah feints after seeing Gorilla]

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