chapter 6 math test terms

yay good luck

perpendicular bisector theorem

if a point is on a perpendicular bisector, then it is equidistant from the endpoints

converse of the perpendicular bisector theorem

if a point is equidistant from the endpoints of the segment, then it is on a perpendicular bisector

angle bisector theorem

if a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle

converse of the angle bisector theorem

if a point is in the interior of an angle and is equidistant from the two sides of the angle, then it lies on the bisector of the angle

circumcenter theorem

the circumcenter of a triangle is equidistant from the vertices of the triangle

circumcenter

meeting point of perpendicular bisectors, circles a triangle

perpendicular bisectors

midpoint and perpendicular, not to vertex

angle bisector

divides an angle evenly, doesnt make two equal segments

incenter

angle bisectors of vertices, makes a circle inside a triangle

incenter theorem

incenter is the same distance to the sides of the triangle

how to find the radius of inscribed circle???

use a perpendicular bisector

median

vertex to midpoint

centroid theorem

vertex to centroid = 2/3 vertex to midpoint

altitude

vertex to opposite side, makes a perpendicular angle, isn’t a midpoint so it’s not congruent segments

where is the circumcenter on an acute triangle??

inside the triangle

where is the circumcenter on a right triangle??

on the triangle

where is the circumcenter on an obtuse triangle??

outside

orthocenter

altitudes of a triangle

where is the orthocenter on an acute triangle??

inside the triangle

where is the orthocenter on a right triangle??

on the triangle

where is the orthocenter on an obtuse triangle??

outside the triangle

where is the centroid on any triangle???

inside the triangle

centroid formula

midpoint formula but it’s with the vertices and you divide by 3

how to find the orthocenter???

find slope for two sides of a triangle, find the perpendicular slopes of those, use point slope to find the equations of the altitudes, solve the system of equations

midsegment

segments that connect the midpoints of two sides of a triangle

midsegment triangle

triangle formed by connecting the midpoints of the sides of a triangle

triangle midsegment theorem

segment connecting midpoints of two sides of a triangle is parallel to the other side (side not being connected), the midsegment is half of the “other side”

how to format an indirect proof?

write all the “eithers,” play devil’s advocate and prove the one that you aren’t actually trying to prove is correct, when you find a contradiction with the given then prove the one you are actually trying to prove is correct, when you have multiple eithers and they can be proven similarly then just say can be proven similarly

triangle longer side theorem

if you have the biggest side, then the angle opposite the biggest side is also the biggest angle

triangle larger angle theorem

if you have the biggest angle, then the side opposite the largest angle is the largest side

triangle inequality theorem

add up two sides of a triangle and it will ALWAYS be bigger than the side not being added

hinge theorem

two sides of two triangles are congruent! the included angle of one triangle is bigger than the other. the one with the bigger angle has a bigger third side

converse of the hinge theorem

two sides are congruent! the third side is larger than the other. the one with the larger side has a larger included angle

centroid

point of concurrency of medians