Studied by 235 peopleMidsegment
Joins two midpoints of two sides of a triangle Parallel and half the length of the 3rd side a triangle
Perpendicular Bisector
The bisector is also perpendicular Equidistant (same distance) from the endpoints of the segments
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Converse of Perpendicular Bisector Theorem
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector
Angle Bisector
A ray, segment, or line, that divides an angle into two congruent angles
Angle Bisector Theorem
If a point is on the bisector of an angle, then it is equidistant from the sides
Converse of Angle Bisector Theorem
If a point in the interior of a triangle is equidistant from the sides of the angle, then it is on the angle bisector
Median
A segment that connects a vertex to midpoint of the opposite side
Alititude
A perpendicular segment that goes from a vertex to the opposite side
Circumcenter
Perpendicular Bisector
Circumcenter Theorem
The circumcenter is equidistant to the vertices of the triangle
Circumcenter location
Acute triangle - inside Obtuse - outside Right - On Same as orthocenter locations
Incenter
Angle Bisector
Incenter theorem
The incenter is equidistant to the sides of the triangle
Incenter/Centroid location
ALWAYS INSIDE
Incenter
Always "in the center", always inside the triangle
Centroid
Median
Centroid Theorem
The centroid is the balancing point of the triangle. 2/3 and 1/3 split of the median (longer one goes from the centroid to the vertex)
Centroid/Incenter location
ALWAYS INSIDE
Orthocenter
Altitude
Orthocenter location
Acute - Inside Obtuse - Outside Right - on Same as circumcenter locations
Triangle Inequality Theorem
The sum of the lengths of any two sides must be greater than the third side (shortcut: add the two shortest lengths and compare to the other side)
Scalene Triangle Inequality
The longest side is opposite the largest angle
The point that is equidistant from the sides of ∆ABC is called the _____.
Incenter
The point that is equidistant from the vertices of ∆ABC is called the _____
Circumcenter
Centroid facts
The point that divides the median into a 2/3, 1/3 split is called the triangle’s _____
In what kind of triangle does the circumcenter lie on of the circle?
Right Triangle
Circumcenter
=dist. to vertices
Incenter
=dist. to sides
Centroid formula
((x1 + x2 + x3)/3, (y1 + y2 + y3)/3)
Note
Flashcard