Chapter 5 Flashcards
Perpendicular Bisector Theorem
If a point is on the perpendicular bisector of the 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
Concurrent Lines
3 or more lines that intersect at a common point
Point of Concurrency
where concurrent lines intersect
Circumcenter Theorem
The perpendicular bisectors of the sides of a triangle are concurrent at a point called the circumcenter that is equidistant from the vertices of a 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 an angle, then it is on the angle’s bisector
Incenter Theorem
The angle bisectors of a triangle are concurrent at a point called the incenter. The incenter is equidistant from the sides of the triangle
Median
-endpoints are a vertex of the triangle and midpoint of the opposite side
Centroid
- always on the interior of a triangle
- “balance point” of the triangle
Centroid Theorem
The medians of a triangle intersect at a point called the centroid that is two-thirds of the distance from each midpoint of the opposite side
Altitude
Perpendicular segment from a vertex to the line containing the opposite side
Orthocenter
Point where all of the altitudes are concurrent
Perpendicular Bisectors
- must be a bisector
- must be perpendicular
- creates 2 congruent
Comparison Property of Inequality
a<b>b</b>
Transitive Property of Inequalities
if a<b>b and b>c, then a>c</b>
Addition Property of Inequality
if a>b, then a+b>b+c
if a <b></b>
Subtraction Property of Inequality
if a>b, then a-c>b-c
if a<b></b>
Exterior Angle Theorem
The measure of an exterior angle of a triangle is greater than either of it’s corresponding remote interior angles
Side- Angle Relationships
If one side of a triangle is larger than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side.
Angle-Side Relationships
If one angle of a triangle is greater in measure than another angle in the triangle, then the side opposite the bigger angle is longer than the side opposite the smaller angle.
Exterior Angle Inequality Theorem
The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.
Triangle Inequality Theorem
The sum of 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 triangle is larger than the included angle of the 2nd triangle, than the 3rd side of the first triangle is larger than the third side of the second triangle
Converse of Hinge Theorem
If 2 sides of a triangle are congruent to 2 sides of another triangle, and the 3rd side in the first triangle is larger than the 3rd side in the second, then the included angle measure of the first triangle is greater than the included angle measure in the 2nd triangle.
