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Chapter 5 Vocab. Geometry
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Gravity
Terms in this set (32)
Median
in a triangle, a line segment with endpoints that are a vertex of a triangle and the midpoint of the side of the opposite vertex
Altitude
in a triangle, a segment from a vertex of a triangle to the line containing the opposite side and perpendicular to that side
Perpendicular Bisector
in a triangle, a line, segment, or ray that passes through the midpoint of a side and is perpendicular to that side
Angle Bisector
a ray that divides an angle into two congruent angles
Concurrent Lines
three or more lines that intersect at a common point
Point of Concurrency
the point of intersection of concurrent lines
Circumcenter
the point of concurrency of the perpendicular bisectors of a triangle
Incenter
the point of concurrency of the angle bisectors of a triangle
Perpendicular Bisector Theorem
if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment
Converse of Perpendicular Bisector Theorem
if a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment
Circumcenter Theorem
the perpendicular bisectors of a triangle intersect at a point called the circumcenter that is equidistant from the vertices of the triangle
Angle Bisector Theorem
if a point is on the bisector of an angle, then it is equidistant from the sides of the angle
Converse of Angle Bisector Theorem
if a point in the interior of an angle is equidistant from the sides of the angle, then it is on the bisector of the angle
Incenter Theorem
the angle bisectors of a triangle intersect at a point called the incenter that is equidistant from the sides of the triangle
Perpendicular Bisector (Special Property)
Circumcenter is equidistant from each vertex (verpendicular)
Angle Bisector (Special Property)
Incenter is equidistant from each side
Median (Special Property)
Centroid is 2/3 of the was to a vertex
Where is circumcenter in perpendicular bisector?
acute- inside, obtuse- outside, right-on
Where is incenter in angle bisector?
acute- inside, obtuse-inside, right- inside
Where is centroid in median?
acute- inside, obtuse-inside, right-inside
Where is orthocenter in altitudes?
acute- inside, obtuse- outside, right- on
Centroid
point of concurrency of the medians of a triangle
Orthocenter
where the lines containing the altitudes of a triangle intersect
definition of inequality
for any real numbers a and b, a > b if and only if there is a positive number c such that a= b +c
If one side of a triangle is longer than the other side
then the angle opposite the longer side has a greater measure than the angle opposite the shorter side
exterior angle inequality
the measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles
indirect reasoning
assuming that a conclusion was false and then showing that this assumption led to a condraction
If one angle of a triangle has a greater measure than another angle
then the side opposite the greater angle is longer than the side opposite the lesser angle
indirect proof (proof by contradiction)
assume hat what you are trying to prove is false, then prove your assumption false and the original conclusion true
Triangle inequality theorem
the sum of the lengths of any two sides of a triangle must be greater than the length of the third side
hinge theorem
if two sides of a triangle are congruent to two sides of another triangle and the included angle of the first is larger than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle
converse of hinge theorem
if two sides of a triangle are congruent to two sides of another triangle, and the third side in the first is longer than the third side in the second triangle then the included angle measure of the first triangle is greater than the included angle measure in the second triangle
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