Chapter 3 Flashcards
Theorem 3.1 midpoint theorem
If M is the midpoint of line AB, than AM = 1/2 AB
Define pustulate 3.2 : Completeness postulate
Given a ray, AB, and any positive real number r, there is exactly one point C on the ray so that AC=r
Define theorem 3.2
The perimeter of a regular n-gon with sides of length s is n•s
Define an equivalence relation
A relation that is reflexive, symmetric, and transitive
Define substitution property
If a=b than a can replace b in any mathematical statement.
Define trichotomy property
For any two real numbers a and b, exactly one of the following is true: a=b, a>b, or a<b
Define ruler postulate
Every point of a line can be placed in correspondence with a real number
Define coordinate of a point on a line
The number that corresponds to the point
the distance between two points A and B
The absolute value of the difference of their coordinates.
Distance between points A and B is denoted by AB, given by AB=|a-b|
A point M is between A and B if
AM+MB=AB. The correct notation is A-M-B
The midpoint of line AB is M if
A-M-B and AM=MB
Define bisector of a segment
A curve that intersects the segment only at the midpoint
Define congruent segments
Segments that have the same length. The symbol ~= is used for congruent segments.
Define perimeter
The distance around a closed curve
Define circumference
The distance around a circle
Define inscribed polygon
A polygon whose vertices are points on a circle
Define inscribed angle
An angle whose vertex is on a circle and whose sides each contain another point of a circle
Define a polygon circumscribed about a circle
A polygon whose sides intersect the circle in exactly one point
Define tangent line (or tangent)
The line in the plane of the circle that intersects the circle in exactly one point
Define the point of tangency
The point at which a tangent line and a circle intersect
Define tangent segment
A segment of a tangent line that contains the point of tangency
