# Triangle centers quiz & similarity review

Editing needed:
explicitly state applications of similar figures (and prerequisite skills for being able to solve for missing side lengths)

WARM UP: For our warm up we went over a few problems from the practice quiz we got the night before.

Next we took our quiz, which looked like this.

"HOW TO DO THIS" SECTION

How to draw the altitude - To draw the altitude of triangle ABC from point C first you would get a compass and put one end on point C, and then draw a semi-circle along line segment AB, if the semi-circle doesnt touch both parts of the line you may need to extend the line segment. Next you should take the compass and draw a small semi-circle from where the other simi-circle touched one point of the line segment, then do the same to the other point of intersection. Then you will draw a line from point C to where the two smaller semi-circles cross.

How to write the equation of a line - First take the quardinates from poin C then plug them into point slope formula which is (y-y) = slope (x-x), then to find the slope, you take the neagative reciprocal of line segment AB, and plug that into the formula, and then you have your equation of a line.

How to find the -
Circumcenter -
To find the circumcenter first you take a compass and put it at any one of the points, then you open the compass so that it is larger then half the segment, then you draw a semi-circle. After that you take the compass and move the point to the other end of that same segment, and you draw another semi-circle. Finally you take your straight edge and you make a line conecting where the two half circles crossed in two different points. After all that you repeat the steps on another segment. Then where the two points cross is the circumcenter. You only need to do this to two segments, not all three.

Orthocenter - To find the orthocenter you will need to draw the altitude twice, you can find how to draw the altitude above in the how to draw the altitude section. The point where the two altitudes cross is the orthocenter.

Incenter - To draw the incenter you will first need to draw at least two angle bisectors. To do this you will need take your compass and put it where two of the lines meet. Then draw a semi-circle touching both lines. After that you will need to take the compass and draw two semi circles one from where the first semi-circle hits a line, and the other on the other side. Then you will need to take your straight edge and make a line from the original point to where the two smaller semi-circles meet. After you have done this twice the point where the two lines you drew cross is the incenter.

Centroid - To draw the centroid you will need to first find the midpoint of at least two of the lines. Then once you have the midpoint you need to connect the midpoint to the point on the oposite side of the line. Then do this at least one more time, then where the two points connect is where the centroid is.

After we took our quiz, we talked about similar triangles:

Similar Triangles

Please make a note that the text in red represent the verticies of the triangle, and that the text in green represent the lengths of the triangle's sides. Also note that the triangles are not drawn to scale.

AB = BC = AC
DF FE DE

<A is congruent to <D

<B is congruent to <F

<C is congruent to <E

Iff (if and only if):

Triangle ABC is similar to Triangle DEF (in geometry, you'd write it as "(Triangle) ABC ~ (Triangle) DEF")

There are two ways to find similar triangles

Way #1: "long-to-long", "short-to-short":

long one = short one
long two short two

Way #2: "long-to-short", "long-to-short":

long 1 = long 2
short 1 short 2

Here's how you'd do this in Way #1

$\frac{8}{20}=\frac{x}{6}$

And here's how you'd do this in Way #2

$\frac{8}{x}=\frac{20}{6}$

Some common mistakes - are confusing the centroid and the cercumcenter. One way to not get them confused is by thinking of the centroid as the center mass meaning that this point is always going to be in the exact center of the triangle.