# Properties of Equality and Congruence

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.

 Congruence Understand congruence in terms of rigid motion Geometry CongruenceCongruence and constructionsProve theorems involving similarityUnderstand congruence in terms of rigid motions Language English Language Similarity, Right Triangles, and Trigonometry Prove theorems involving similarity Triangles Congruent Triangles

### 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]