Term

Definition
The set of all points Pg. 6 


Term

Definition
Points all in one line Pg. 6 


Term

Definition
Points all in one plane Pg. 6 


Term

Definition
Where two figures(lines, planes, or the combination of both) meet or cut. The set of points that are in both figures. Pg. 6 


Term

Definition
Shown by two letters(the endpoints) with a line over it. Constists of the endpoints and all points between those endpoints. Pg. 11 


Term

Definition
Shown by two letters(one an endpoint named first and another) with an arrow going to the right over the top. Consists of the endpoint and all points to and paste the second letter. Pg. 11 


Term

Definition
Rays that start at the same endpoint, but go in opposite direction. Pg. 11 


Term

Definition
Shown by two letters(the endpoints). Subtract the coordinates of it endpoints. Pg. 11 


Term

Definition
Statements that are accepted wihout proof Pg. 12 


Term

Definition
1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinantes 0 and 1. 2. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates. Pg. 12 


Term
Segment Addition Postulate 

Definition
If B is between A and C, then AB + BC = AC PG. 12 


Term
Congruent and Congruent Segments 

Definition
Two objects that have the same size and shape. Two segements that have equal length. Pg. 13 


Term

Definition
The point that divides the segment into two congruent segements. Pg. 13 


Term

Definition
A line, segment, ray, or plane that intersects the segment at its midpoint. Pg. 13 


Term

Definition
The figure formed by two rays that have the same endpoint. Pg. 17 


Term
Sides &Vertex of an angle 

Definition
Sides  the two rays that form the angle Vertex  the common endpoint of the rays that form the angle Pg. 17 


Term

Definition
Measure between o and 90 Pg. 17 


Term

Definition


Term

Definition
Measure between 90 and 180 Pg. 17 


Term

Definition


Term

Definition
On line AB in a given plane, choose any point 0 between A and B. Consider line OA and line OB and all the rays that can be drawn from o on one side of line AB. These rays can be paired with the real numbers from 0 to 180 in such a way that: a. Line OA is paired with 0, and line OB with 180. b. If line OB is paired with x, and line OQ with y, then m ‹ POQ = ǀxyǀ Pg. 18 


Term

Definition
If point B lines in the interior of <AOC, then m< AOB + m< BOC = m< AOC If < AOC is a straight angle and B is any point not on line AC, then m< AOC + m< BOC = 180 Pg. 18 


Term

Definition
Angles that have equal measures Pg. 19 


Term

Definition
Two angles in a plane that have a common vertex and a common side but no common interior points Pg. 19 


Term

Definition
The ray that divides that angle inot two congruent adjacent angles. Pg. 19 


Term
Postulate 5 # of points in a line 

Definition
A Line contains at least two points; a plane contains at least three points not all in one line; space contaoins at least four points not all in one plane. Pg. 23 


Term
Postulate 6 Forming a line 

Definition
Through any two points there is exactly one line. Pg. 23 


Term
Postulate 7 # of points in a plane 

Definition
Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane. Pg. 23 


Term
Postulate 8 Lines in a plane 

Definition
If two points are in a plane, then the line that contains the points is in that plane. Pg. 23 


Term
Postulate 9 Intersecting planes 

Definition
If two planes interest, then their intersection is a line. Pg. 23 


Term
Theorem 11 Intersecting lines 

Definition
If two lines intersect, then they intersect in exactly one point. Pg. 23 


Term
Theorem 12 Forming a plane 

Definition
Through a line and a point not in a line there is exactly one plane. Pg. 23 


Term
Theorem 13 Intersecting lines and planes 

Definition
If two lines intersect, then exactly one plane contains the lines. Pg. 23 


Term
IfThen Statements Conditional Statements or conditionals 

Definition
Example: If B is bewtween A and C, then AB + AC =AC or If p, then q Pg. 33 


Term

Definition
The if part of an ifthen statement Pg. 33 


Term

Definition
The then part of an ifthen statement Pg. 33 


Term

Definition
When the hypothesis and conclusion are interchanged Pg. 33 


Term

Definition
When an example can be found where the hypothesis is true and the conclusion is false. Pg. 33 


Term

Definition
When a conditional and is converse are both true they can be combined into a single statement. A statement that contains the words "if and only if" Pg. 34 


Term

Definition
If a = b and c = d, then a + c = b +d This can also be used to add a number to both sides. Example: a + 2 = b + 2 Pg. 37 


Term

Definition
If a = b and c =d, then a  c = b + d This can also be used to subtract a number from both sides Example: a  2 = b  2 Pg. 37 


Term

Definition
If a = b and c = d, then a c = b d This can also be used to multiply both sides of the equation by the same number. Example: 1/2a = 1/2b Pg. 37 


Term

Definition
If a = b and c ≠ 0, then a/c = b/c Pg. 37 


Term

Definition
If a =b, then either a or b may be substituted for the other in any equation (or inequality) Pg. 37 


Term

Definition


Term

Definition
If a = b, then b = a or If < D ≅ < E, then < E ≅ < D Pg. 37 


Term

Definition
If a = b and b = c, then a =c or If < D ≅ < E and < E ≅ < F, the < D ≅ < F Pg. 37 


Term

Definition


Term

Definition
If M is the midpoint of seg AB, then AM = 1/2AB and MB = 1/2AB Pg. 43 


Term

Definition
If Ray BX is the bisector of < ABC, then m< ABX = 1/2m< ABC and m< XBC = 1/2m< ABC Pg. 44 


Term

Definition
Given Information Definitions Postulates Properties of Equality or Congruency Theorems (that have already been proved) Pg. 45 


Term

Definition
Two angles whose measures have the sum of 90 Each angle is called a complement of the other. Pg. 50 


Term

Definition
Two angles whose measures have the sum of 180. Each angle is called asupplement of the other. Pg. 50 


Term

Definition
Two angles that have sides consisting of opposite rays. When two lines interest, they form two pairs of vertical angles. Pg. 51 


Term

Definition
Vertical angles are Congruent Pg. 51 


Term
Theorem 24 If two lines are ┴, then ___________ 

Definition
If two lines are perpendicular, then they form congruent adjacent angles. Pg. 56 


Term
Theorem 25 If two lines form ≅ adj. <'s, then ________ 

Definition
If two lines form congruent adjacent angles, then the lines are perpendicular. Pg. 56 


Term
Theroem 26 If the ext. sides of two adj. actue <'s are ┴, then ________ 

Definition
If the exterior sides of two adjacent acute angles are perpendicular, then the angls are complementary. Pg. 56 


Term

Definition
Two lines that intersect to form right angles. Pg. 56 


Term
Theorem 27 Supplements of ≅ <'s 

Definition
If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent. Pg. 61 


Term
Theorem 28 Complements of ≅ <'s 

Definition
If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent. Pg. 61 


Term
Parrallel Lines Parrallel Planes 

Definition
Are coplanar lines that do not intersect.
Planes that do not intersect Pg. 73 


Term

Definition
Are noncoplanar lines, that are neither parallel or intersecting Pg. 73 


Term
A line and plane are Parallel 

Definition
If they do not intersect Pg. 73 


Term
Theorem 31 If two ǁ planes are cut by a third plane, then _________ 

Definition
If two parallel planes are cut by a third plane, then the lines of intersection are parallel. Pg. 74 


Term

Definition
A line that intersects two or more coplanar lines in different points. Pg. 74 


Term

Definition
Two nonadjacent interior angles on opposite sides of the transversal. Pg. 74 


Term
SameSide Interior Angles 

Definition
Two interior angles on the same side of the transversal. Pg. 74 


Term

Definition
Two angles in corresponding positions relative to the two lines. Pg. 74 


Term
Postulate 10 Correspoinding <'s 

Definition
If two parallel lines are cut by a transversal, then correspoinding angles are congruent. Pg. 78 


Term
Theorem 32 Starting with ǁ lines 

Definition
If two parallel lines are cut by a transversal, then alternate interior angles are congruent. Pg. 78 


Term
Theorem 33 Starting with ǁ lines 

Definition
If two parallel lines are cut by a transversal, then sameside interior angles are supplementary. Pg. 79 


Term
Theorem 34 If a transversal is ┴ to one of two ǁ lines, then _______ 

Definition
If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other one also. Pg. 79 


Term
Postulate 11 Converse to corr. <'s (Post. 10) 

Definition
If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Pg. 83 


Term
Theorem 35 Starting with alt. int. <'s 

Definition
If two lines are cut by a transversal and alt. int. angles are congruent, then the lines are parallel. Pg. 83 


Term
Theorem 36 Starting with sameside int. <'s 

Definition
If two lines are cut by a transversal and sameside interior angles are supplementary, then the lines are parallel. Pg. 84 


Term

Definition
In a plane two lines are perpendicular to the same line are parallel. Pg. 84 


Term

Definition
Through a point outside a line, there is exactly one line paralllel to the given line. Pg. 85 


Term

Definition
Through a point outside a line, there is exactly one line perpendicular to the given line. Pg. 85 


Term
Theorem 310 Three ǁ lines 

Definition
Two lines parallell to a third line are parallel to each other. Pg. 85 


Term
Ways to Prove Two Lines Parallel 

Definition
Show corr. <'s are ≅ Show alt. int. <'s are ≅ Show sameside int. <'s are supp. Show both lines are ┴ to a third line Show both lines are ǁto a third line. Pg. 85 


Term

Definition
The figure formed by three segments joining three noncollinear points. Pg. 93 


Term
Vertex & Sides of a triangle 

Definition
Vertex  each of the three points of the triangle (Pluural: Vertices) Sides  The segments of a triangle Pg. 93 


Term

Definition


Term

Definition
At least two sides congruent Pg. 93 


Term

Definition
All sides congruent Can also be considered isosceles Equilateral triangle is also equiangular Pg. 93 


Term

Definition


Term

Definition
One obtues < A triangle can not have more then one obtuse < Pg. 93 


Term

Definition
One right < A triangle can not have more than one right < Pg. 93 


Term

Definition
All <'s congruent Equiangular triangles are also equilaterial Pg. 93 


Term
Theorem 311 Sum of the int. <'s of a ∆ 

Definition
The sum of the measure of the angles of a triangle is 180 Pg. 94 


Term
Corollary 1, 2, 3 & 4 of Theorem 311 

Definition
1. If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent 2. Each angle of an equiangular triangle has measure 60 3. In a triangle, there can be at most one right angle or obtuse angle 4. The acute angles of a right triangle are complementary. Pg. 94 


Term
Theorem 312 Ext. < of a ∆ 

Definition
The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles. Pg. 95 


Term

Definition
A line, ray, or segement added to a diagram to help in a proof. Pg. 94 


Term

Definition
Means "many angles". Any figure with three or more sides having the two qualitiles below. 1. Each segment intersects exactly two other segements, one at each endpoint 2. No two segments with a common endpoints are collinear Pg. 101 


Term

Definition
A polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. Pg. 101 


Term

Definition
3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 8 Octagon 10 Decagon n ngon Pg. 101 


Term

Definition
A segment joining two nonconsecutive vertices of a polygon. Pg. 102 


Term
Theorem 313 Sum of int. <'s of a polygon 

Definition
The sum of the measures of the angles of a convex polygon with n sides is (n2)180 Pg. 102 


Term
Theorem 314 Sum of ext. <'s of a polygon 

Definition
The sume of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360. Pg. 102 


Term

Definition
A polygon that is both equiangluar and equlateral. Pg. 103 


Term

Definition
Conclusion based on accepted statements (definitions, postulates, previous theorems, corolaries, and given information) Conclusion must be true if hypotheses are true. Pg. 106 


Term

Definition
Conclusion based on several past observations Conclusion is probably true, but not necessarily true. Pg. 106 

