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Properties of Equality and Congruence 3671 Views
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Description:
You have to feel bad for goats whose horns are in the shape of polygons. You just know they got ridiculed for it back at Goat High. Kids can be so cruel.
- Geometry / Congruence
- Geometry / Understand congruence in terms of rigid motions
- Geometry / Prove theorems involving similarity
- Geometry / Congruence and constructions
- Congruence / Understand congruence in terms of rigid motion
- Similarity, Right Triangles, and Trigonometry / Prove theorems involving similarity
Transcript
- 00:03
properties of equality and congruence a la shmoop
- 00:06
here we see except that their horns twist and branch in various sharp angles [goats on mountain]
- 00:24
usually farming polygons today wildlife researcher and go-to expert Sarah Nevada [goat's horns form polygons]
- 00:31
intends to bust the local myth that no two mountain goats horns will ever grow [goats in a field]
- 00:35
into the same shape aha it seems sarah has found three [three goats with triangle horns]
Full Transcript
- 00:40
candidates whose horns at first glance grow in about the same shape we'll call
- 00:45
these goats a B and C let's get a close-up on those warrants how does
- 00:51
Sarah determine if the shapes of the goats horns are identical or in
- 00:55
geometric terms congruent goat A's horns grow in a triangle shape let's label the [woman on mountain top]
- 01:01
points of the triangle X sub a y sub T and Z sub a from these measurements we [goat with triangle horns]
- 01:09
can draw the definite conclusion the triangle X sub a y sub a Z sub a is
- 01:13
congruent to triangle X of a y sub a Z sub a when a geometric element is equal
- 01:20
to itself it's demonstrating the reflexive property of congruence now
- 01:26
let's move on to goat B's horns which also grow in a triangle shape let's
- 01:30
label the points X sub B Y sub P and Z sub P Sara's hoping that goat a and goat
- 01:36
B's horns form the same triangle thereby refuting the myth if triangle a is [both goats together]
- 01:42
congruent to triangle B we can conclude the triangle B is congruent to triangle
- 01:47
a this demonstrates the symmetric property of congruence which illustrates
- 01:52
that equality is a two-way street now triangle a is congruent to triangle [cars driving past each other]
- 01:57
B we can look at goat C's likewise triangular horns and follow the same
- 02:01
logic the triangle C is congruent to triangle B and we've previously
- 02:06
established the triangle V is common - triangle a we can conclude the
- 02:11
triangle C is also congruent to triangle a this series of equalities demonstrates
- 02:18
the transitive property of congruence the geometric properties of equality and
- 02:23
congruence are pretty intuitive but it's important to know that they exist
- 02:28
unfortunately for Sarah the go-to expert she's just come across an undercoat or [goat chases Sarah]
- 02:32
rather threatening for information' maybe she'll study gorilla [Sarah feints after seeing Gorilla]
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