unit 5 Flashcards
Ruler postulate:
the points on a line can be matched with real numbers such that the distance between 0 and 1 is 1 unit length. All other real numbers on that line are based on that given distance. For example, 2 is twice the given unit length
Coordinate
The real number corresponding to the position of a point on a number line or coordinate plane
Slope
The ratio of the change in y over the change in x
Slopes of parallel lines theorem
in a coordinate plane, two distinct non-perpendicular lines have the same slope if they are parallel
Parallel postulate
If there is a line and a point not on the line, then there is exactly one line through the point parallel at any given time
Perpendicular postulate:
If there is a point and a point not on the line, then there is exactly one line through the point perpendicular to the given line.
Perpendicular bisector
A ray, line, or segment is a perpendicular bisector if and only if it intersects a segment at the midpoint perpendicularly
Distance from point to a line
The dostamce netweem a point and a line is always the shortest distance possible which is perpendicular to the line from that point.
Partitioning
Dividing or splitting into small parts
Midpoint formula
mx = (x1/2 + x2/2) my= (y1/2 + y2/2)
Distance Formula
d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}
Polygon
A closed plane figure formed by three or more segments called (sides).
Convex polygon
A polygon is a convex polygon if and only if and only if no line that contains a side of the polygon also includes a point in the interior of the polygon
Concave polygon
A polygon is a voncave polygon if and only if it has at least one line that contains a side that also intersects with one or more points that lie within the interior of the polygon.
Perimeter
the total length of all sides of a polygon
Area
The number of square units that fill the space on the interior of a planar figure.
Midsegment of a triangle
A segment is a midsegment of a triangle, if and only if its endpoints are the midpoints of two sides of the triangle
Triangle midsegment theorem
A segment is a midsegment; it is (1) parallel to the third side and (2) its length is equal to half the length of the third side.
Altitude of a triangle
A segment is an altitude if and only if it has one endpoint as a vertex and the other on the side opposite that vertex and it intersects that side perpendicularly
The median of a triangle
A segment is a median of a triangle if and only if it has one endpoint as a vertex and the other endpoint at the midpoint on the side opposite the vertex>
