Chapter 5- Altitudes, Medians, Etc Flashcards
Line that connects midpoint to midpoint
Midsegment
Connects midpoint to opposite angle
Median
Line that goes through the midpoint of a side and is perpendicular to that same side
Perpendicular bisector
Line that goes through an angle, and is perpendicular to opposite side. (Measures/determines height)
Altitude
Midsegment theorem
The midsegment is half the length as the third side, parallel to it
Perpendicular bisector theorem
Converse to theorem
If a point is on the perpendicular bisector, then it is equidistant from the end points.
If a point is equidistant from the end points, it is on the perpendicular bisector
What is the point of concurrency
The point of intersection of three or more lines
Where is the point of concurrency on an acute angle? Right angle? Obtuse angle?
Acute-inside
Right-on the midpoint of the hypotenuse
Obtuse-outside the triangle
Concurrency of perpendicular bisectors of a triangle
The perpendicular bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle
What is the name of the point that 3 angle bisectors meet at?
Incenter
Angle bisector theorem
Converse to theorem
If a point is on the bisector of an angle, then it is equidistant from the two sides of the triangle
If a point is equidistant from the two sides, it is on the angle bisector
Name of point where 3 medians meet?
What is the rules with lengths of segments between sides and centroid?
Centroid. The line that is from the vertex to the centroid is double the length of the segment from the side to the centroid. (In thirds)
Name of point where 3 altitudes meet?
Location of orthocenter for acute, right, obtuse?
Orthocenter.
Acute-inside
Right-vertex of the right angle
Obtuse-outside
Triangle inequality theorem
The sum of the lengths of any two sides of a triangle is greater than the third side.
