Chapter 5 voc. Flashcards
The point at which they intersect
Point of concurrency
The point of concurrency of the perpendicular bisectors of a triangle is called the _____________
Circumcenter of a triangle
Something you say p.301
Circumscribed about
The point of concurrency of the angle bisectors of a triangle is called the ______
Incenter of a triangle
Is a length of the perpendicular segment from the point to a line
Distance from a point to a line
In _________ all possibilities are considered and then all but one are proved false
Indirect reasoning
Is a segment whose end points are a vertex and the midpoint of the opposite side
Median of a triangle
The point of concurrency of the medians is the __________
Centroid of a triangle
Is the perpendicular segment from a vertex of the triangle to the line containing the opposite sides
Altitude of a triangle
A proof involving indirect reasoning is an _______ ________
Indirect proof
Where three or more lines intersect at one point
Concurrent
The center of the the circle that is _______ ____ the triangle
Inscribed in
The lines that contain the altitudes of a triangle are concurrent at the ________
Orthocenter of a triangle
A segment connecting the midpoints of two sides of the triangle
Mid segment of a triangle
The medians of a triangle are concurrent at a point that is 2/3 the distance from each vertex to the midpoint f the opposite side
Theorem 5-8 concurrency of medians theorem
A point is ________ from two objects if it is the same distance from the objects
Equidistant
If a point is equidistant from the endpoint of a segment, the. It is on the perpendicular bisector of the segment
Theorem 5-3 converse of the perpendicular bisector theorem
If a point is on he bisector of an angle, then the point is equidistant from the sides of the angle
Theorem 5-4 angle bisector theorem
If a point in the interior of a. Angle is equidistant from the sides of the angle, then the point is on the angle bisector
Theorem 5-5 converse of the angle bisector theorem.
The lines that contain the altitudes of a triangle are congruent
Theorem 5-9 concurrency of altitudes theorem
The perpendicular bisectors of the sides of a triangle are concurrent at a point equidistant from the vertices
Theorem 5-6 concurrency of perpendicular bisectors theorem
If two sides of atria gale are not congruent, then the larger angle lies opposite the longer side
Theorem 5-10
If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle
Theorem 5-11
If two sides of one triangle are congruent to two sides of another triangle, and the included angles are not congruent, then the longer third side is opposite the larger included angle
Theorem 5-13 the hinge theorem (SAS inequality theorem)
If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side and is half as long
Theorem 5-1 triangle mid segment theorem
The sum of the lengths of any two side of a triangle is greater than the length of the third side
Theorem 5-12 triangle inequality theorem
If a points on the perpendicular bisector of a segment, the I it is equidistant from the end points of the segment
Theorem 5-2 perpendicular Bisector theorem
The bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle
Theorem 5-7 concurrency of angle bisectors theorem
