Chapter 5 Flashcards
49 perpendicular bisector thrm
if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints on that segment
50 conv of perpendicular bisector thrm
if a point is equidistant from the endpoints on that segment, then it is on the perpendicular bisector of a segment
51 angle bisector thrm
if a point is on an angle bisector, then it is equidistant from rays of angle
52 conv of angle bisector thrm
if a point is equidistant from rays of angle, then it is on an angle bisector
53 concurrency of perpendicular bisectors
the perpendicular bisectors of sides of a triangle are concurrent at a point equidistant from the verticies
(circumcenter/circumcircle)
54 concurrency of the angle bisectors
the bisectors of the angles of a triangle are concurrent at a point equidistant from the sides of the triangle
(incenter/incircle)
55 concurrency of medians
the medians of a triangle are concurrent at the point that is 2/3 the distance from each vertex to the midpoint of the opp side
(centroid)
56 concurrency of altitudes
the lines that contain the altitudes of a triangle are concurrent
(orthocenter)
57 side to angle inequality in one triangle thrm
if 2 sides of one triangle are not congruent, then the larger angle lies opp the longer side
58 conv of side-angle inequality in one triangle
if 2 angles of a triangle are not congruent, then the longer side lies opp to the larger angle
59 triangle inequality thrm
the sum of lengths of any two sides of a triangle is greater than the length of the 3rd side
60 hinge thrm
if 2 sides of a triangle are congruent to 2 sides of another triangle, and included angles are not congruent, then the longer side is opp to the larger included angle
61 conv to hinge thrm
if 2 sides of a triangle are congruent to 2 sides of another triangle, and third sides are not congruent, then the larger included angle is opp to the longer 3rd side
62 properties of inequalities - comparison
if a = b + c,
where a, b, c, > 0,
then a > b, a > c
