Chapter 1 - Building Blocks Flashcards
Become familiar with the vocabulary, meaning, and formulas that we use in this course.
Point
A location in a plane or in space, having no dimensions. Represent as a dot. Name it by a capital letter such as A
(pg. 11)
Line
A straight set of points that extends into infinity in both directions. Name it by any 2 points on the line, or by single lowercase letter
(pg. 11)
(Line) Segment
Two points on a line, and all the points between those two points. Name it by any 2 endpoints on the segment
(pg. 12)
Ray
Part of a line, containing one endpoint and extending to infinity in one direction.
(pg. 12)
Opposite Rays
Opposite rays are collinear rays with the same endpoint. They form a line.
(pg. 12)
Collinear
Points are collinear if they lie on the same line.
Plane
Represented by a flat surface that extends without end and has no thickness. Name it by a capital letter or by at least 3 points in the plane that are not collinear.
(pg. 11)
Postulate or Axiom
Is an accepted statement of fact. Basic building block of the logical system of geometry.
(pg. 13)
Postulate 1-1
Through any two points there is exactly one line.
pg. 13
Postulate 1-2
If two distinct lines intersect they intersect in exactly one point.
(pg. 13)
Postulate 1-3
If two distinct planes intersect they intersect in exactly one line.
(pg. 14)
Postulate 1-4
Through any three noncolliner points there is exactly one plane.
(pg. 15)
Ruler Postulate
Every point on a line can be paired with a real number. The real number that corresponds to a point is called the coordinate of that point.
(pg. 20)
Segment Addition Postulate
If three points A, B, & C are collinear and B is between A & C, then AB + BC = AC
(pg. 21)
Congruent Segments
If segments have the same length they are congruent.
pg. 22
Congruent
Angles or figures that have the same size and shape.
(Segment) Midpoint
A midpoint of a segment is the point that divides the segment into two congruent segments.
(pg. 22)
(Segment) Bisector
A point, line, ray or segment that intersects a segment at it’s midpoint.
(pg. 22)
Angle
An angle is formed by two rays that start at a common endpoint.
(pg. 27)
Vertex
The common endpoint of the two rays that make up an angle.
pg. 27
Naming Angles
(pg. 27)
By it’s vertex (Angle A), a point on each ray and the vertex (Angle BAC or Angle CAB), a number (Angle 1)
Acute Angle
0 < angle < 90
pg. 29
Right Angle
angle = 90
pg. 29
Obtuse Angle
90 < angle < 180
pg. 29
Straight Angle
(pg. 29)
angle = 180
Congruent Angle
Angles with the same measure.
pg. 29
Angle Addition Postulate
If point B is in the interior of angle AOC then m angle AOB + m angle BOC = m angle AOC.
(pg. 30)
Adjacent Angles
Two coplanar angles with a common side, a common vertex, and NO common interior points
(pg. 34)
Vertical Angles
Two angles whose sides are opposite rays.
pg. 34
Complementary Angles
Two angles whose measures have a sum of 90. Each angle is called the compliment of the other.
(pg. 34)
Supplementary Angles
“(pg. 34) Two angles whose measures have a sum of 180. Each angle is called the supplement of the other.”
Linear Pair Postulate
“(pg. 36) If two angles form a linear pair then they are supplementary.”
Perpendicular Lines
Two lines that intersect to form right angles.
pg. 44
Perpendicular Bisector
Of a segment is a line segment or ray that is perpendicular to the segment at it’s midpoint.
(pg. 44)
Midpoint (Line)
The coordinate of the midpoint is the average or mean of the coordinate of the endpoints.
(pg. 50)
Midpoint (Plane)
The coordinate of the midpoint is the average or mean of the coordinate of the endpoints.
(pg. 50)
Midpoint (Plane)
The coordinate of the midpoint is the average or mean of the coordinate of the endpoints. Point is average of x-coordiantes and average of y-coordinates.
(pg. 50)
Midpoint (Formula)
M = (x1 + x2)/2 and (y1 + y2)/2 for points in plane, and (a + b)/2 for points on a nunmber line. HINT; x & y coordiantes are on the number line of the x-axis and y-axis
(pg. 50)
Distance Formula
d = sqrt [(x2 - x1)^2 + (y2 - y1)^2]
pg. 52
Perimeter
P of all polygons is the sum of the side lengths.
pg. 59
Area
A is the number of square unit enclosed by a polygon.
pg. 59
Square
If side length = s, P = 4S, & A = s^2
pg. 59
Triangle
If side length = a, b, & c with a base of b & height of h then P = a + b + c and A = (1/2)bh
(pg. 59)
Rectangle
If side lengths are b & h then P = 2b + 2h or 2(b + h) and A = bh
(pg. 59)
Circle
radius = r and diameter = d (or 2r) then C = (pi)d or 2(pi)r and A = (pi)r^2
(pg. 59)
Circumference
C is the Perimeter of a circle.
pg. 59
Area Addition Postulate
The area of a region is the sum of the areas of its nonoverlapping parts.
(pg. 63)
