Students

Teachers & SchoolsStudents

Teachers & SchoolsYou 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.

Congruence | Understand congruence in terms of rigid motion |

Geometry | Congruence Congruence and constructions Prove theorems involving similarity Understand congruence in terms of rigid motions |

Language | English Language |

Similarity, Right Triangles, and Trigonometry | Prove theorems involving similarity |

Triangles | Congruent Triangles |

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

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

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

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

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

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

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

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

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

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

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

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

a this demonstrates the symmetric property of congruence which illustrates

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

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

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

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

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

the transitive property of congruence the geometric properties of equality and

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

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

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