Chapter 5 Flashcards
If a segment joins the midpoint of two sides of a triangle then the segment is parallel to the third side and is half the length
Triangle mid segment theorem
Segment connecting the midpoint of two sides
Mid segment of a triangle
When proving mid segment theorem use coordinates, geometry, and algebra
Coordinate proof
X1+x2,y1+y2
______ ______
2 2
Midpoint formula
Square root of (x2 - x1) squared plus (y2 - y2) squared
Distance formula
If a point is on the perpendicular bisector of a segment then it is equidistant from the endpoints of the segment
Perpendicular bisector theorem
If a point is equidistant from the endpoints of a segment then it is on the perpendicular bisector of the segment
Converse of perpendicular bisector theorem
If a point is on the bisector of an angle tenge point is equidistant from the sides of the angles
Angle bisector theorem
If a point in the interior angle is equidistant from the sides of the angles then the point is on the angle bisector
Converse of angle bisector theorem
Length of the perpendicular segment from the point to the line
Distance form point to line
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices
Theorem 5-6
The bisectors of the angle a of a triangle are concurrent at a point equidistant from the sides
Theorem 5-7
When three or more lines intersect at one point
Concurrent
The point at which the concurrent is
Point of concurrency
The point of concurrency is called this
Circumvented of triangle
The medians of the triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side
Theorem 5-8
The point of congruency of medians
Centroid
Segment whose endpoints are a vertex and the midpoint of the opposite sides
Median of a triangle
Perpendicular segment from a vertex to the line containing the opposite side
Altitude
This of a statement has opposite truth value
Negation
This of a conditional statement negates hypothesis and conclusion
Inverse
This of a conditional statement switches hypothesis and conclusion and negates both
Contra positive
Statements that have same truth value
Equivalent statements
The three perpendicular bisectors f the sides of a triangle meet at this
Circumcenter
The circle that if circles around circumcenter
Circumscribe
Point at which three bisectors of the interior angles of the triangle meet
Incenter
Goes around the incenter
Inscribed circle a.k.a incircle
Point at which the three medians meet
Centroid
Point of intersection of the altitudes of a triangle, the perpendicular lines between each vertex and the opposite side
Orthocenter
