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# geometry

### math stuff

TermDefinition
what is the Circumcenter? It is equidistant from the three vertices
how do you find the circumcenter? Bisect the three sides, the place where they all meet is the circumcenter
what is the incenter? Equidistant from the sides of the triangle
how do you find the incenter? BIsect the tree angles, the place where they all meet is the incenter
what is the orthocenter? where the three altitudes intersect
how do you find the orthocenter? find the three altitudes
on an acute triangle where is the circumcenter? inside
on an obtuse triangle where is the circumcenter? outside
on a right triangle where is the circumcenter? on the hypotenuse
on any triangle where is the incenter? it is always in the inside
what is the median? a line segment from the vertex to the midpoint of the opposite side
what is the centroid? where the three medians intersect
how do you find the centroid? x1+x2+x3 , y1+y2+y3 ̅ ̅ ̅ ̅ ̅ ̅ ̅3 ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅3 ̅ ̅ ̅ ̅ ̅ ̅ ̅
what is altitude? a perpendicular line segment from one side to the opposite vertex
where are the altitudes on an acute triangle? all inside
where are the altitudes on an obtuse triangle? 1 inside, 2 outside
where are the altitudes on a right triangle? 1 inside, 2 on the legs
a² + b² > c² What kind of triangle is this? acute
a² + b² < c² What kind of triangle is this? obtuse
a² + b² = c² What kind of triangle is this? right
On a 45,45,90 triangle you are given one of the legs (X) how do you find the hypotenuse? X√2
On a 45,45,90 triangle you are given the hypotenuse (X) how do you find the legs? X√2/2 (x rad 2 over 2)
On a 30,60,90 triangle you are given the short leg (x), how do you find the long leg and hypotenuse? Long: X√3 .......... Hypotenuse: 2X
On a 30,60,90 triangle you are given the hypotenuse (X), how do you find the long and short legs? Short: X/2 ............. Long: X√3 /2
On a 30,60,90 triangle you are given the long leg (X), how do you find the short leg and hypotenuse? Short: X√3/3 ........... Long: 2X√3/3
Created by: cosettegiroux