Chapter 5 Flashcards
Perpendicular bisector converse
If a point is equidistant from the end points of a segment than it lies on the perp bisector of the segment
Perpendicular bisector Thm
If a point is on the perpendicular bisector of a segment then it is equidistant from the endpoints of its segments
Angle bisector Thm
If a point is on a bisector of an angle then it is equidistant from the two sides of the triangle
Angle bisector converse
If the point is on the interior of the angle and equidistant from the sides of the angle then it lies on the bisector of the angle
Distant between a point and a line
Is the length if the perp seg from the point of the line
Perpendicular bisector
A segment that is part of a perp bis of one of the sides
Angle bisector of a triangle
A segment that bisects one of the angles of the triangle
Median
A segment who’s endpoints are a vertex and the midpoint of the opposite side
Altitude
A segment from a vertex that is perpendicular to the opposite side or to the line containing the opposit side
*an altitude may lie outside or inside of a triangle
Concurrent
A set of lines that a single point of intersection
Circumcenter
A common point of the triangle o the perp bisector
*the circumvented is equidistant from the three vertices of a triangle
Incenter
Angle bisectors common point in a triangle
*the in center is equidistant from the three sides of the triangle
Centroid
The medians common point of a triangle
*the centriod is 2/3 the distance from the vertex to the midpoint of he opposite side
Orthocenter
Altitudes common point of a triangle
*no thms
The lines containing the perp bisector of a triangle are
Concurrent
The concurrent lines common point is the
Circumcenter of a triangle
The circumcenter is ———– from the vertices
Equidistant
The angle bisectors of a triangle are
Concurrent
The Incenter is ———- from the triangles three sides
Equidistant
The medians of a triangle are
Concurrent
Common point =
Centroid
Theorem 5.8
If one angle I a triangle is larger than another angle, Jen the opposite side the larger angle is longer then the side opposite the smaller angle
Centroid is —/— each vertex the the ———- of the opposite side
2/3
Midpoint
The lines containing he altitudes are
Concurrent
Perpendicular bisector of a triangle
A segment that is part of a perpendicular bisectors of one of the sides
Common point =
Orthocenter
Midsegment
The segment thy connects the midpoints of two sides of a triangle
Midsegment theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half it’s length
Theorem 5.7
If one side of a triangle is longer than the other side, then the angle opposite the longer side is larger than the angle opposite I he shorter side
Hinge theorem
If two sides one triangle are congruent to two sides of a second triangle, an the included angle of the first triangle is larger than the included angle of the second, than the included angle of the first is larger than the included angle of the second
Converse of the hinge theorem
If two sides of one triangle are congruent to another triangle, ad the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included able if the secondhand
Triangle inequality theorem 5.9
The sum of the lengths of any two sides of a triangle is greater the. The length of the third side
