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Geometry chapters 1-3 Vocabulary
n/a
60
Mathematics
10th Grade
11/01/2012

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Term
Conjecture
Definition
An unproven statement based on observations
Term
Counter Example
Definition
An example that shows the conjecture is false.
Term
Collinear points
Definition
3 or more points that lie on the same line.
Term
Coplanar points
Definition
4 or more points that lie on the same plane.
Term
Opposite rays
Definition
Two rays that connect at a middle point.
Term
Postulate
Definition
A rule that is accepted without proof.
Term
Ruler postulate
Definition
Points on a line that can be matched up with real numbers.
Term
Segment Addition postulate
Definition
If B is between A and C, then AB + BC = AC
Term
Congruent segments
Definition
Segments that have the same length.
Term
Angle
Definition
Two rays with the same initial point.
Term
Congruent Angles
Definition
Angles that have the same measure.
Term
protractor Postulate
Definition
Each angle has a measure from 0 degrees to 180 degrees.
Term
Angle Addition postulate
Definition
Part + Part = whole m
Term
Adjacent Agnles
Definition
Share a common vertex and a common interiorside.
Term
Midpoint of a segment
Definition
The point that divides the segment into two congruent parts.
Term
Segment Bisector
Definition
Any segment, ray, line of plane, that goes through the midpoint of a segment.
Term
Angle Bisector
Definition
A ray that divides an angle into two congruent adjacent angles.
Term
vertical Angles
Definition
Angles whose sides form two pairs of opposite rays
Term
Linear pair
Definition
Two adjacent angles that form a straight line.
Term
Complementary angles
Definition
Two angles whose sum is 90 degrees
Term
Supplementary Angles
Definition
Two angles whose sum is 180 degrees.
Term
Perpendicular lines
Definition
Two lines that intersect and form a right angle.
Term
Line perpendicular to a plane
Definition
A line that intersects a plane in a point
Term
Law of detachment
Definition
If p->q is true, and p is true, then q is true.
Term
Law of syllogism (Transitivity)
Definition
If p->q and q->r, are both true,then p->r is true.
Term
Law of the contrapositive
Definition
If a conditional p->q is true, then it's contrapositive, ~q->~p is also true.
Term
Addition property
Definition
If a=b then a+c=b+c
Term
Subtraction Property
Definition
If a=b then a-c=b-c
Term
Multiplication Property
Definition
If a=b then a*c = b*c
Term
Division Property
Definition
If a=b, then a/c = b/c
Term
Substitution Property
Definition
If you know the value of a variable, then you can plug it in.
Term
Reflexive Property
Definition
a=a
Term
Symmetric property
Definition
If a=b, then b=a
Term
Transitive property
Definition
If a=b and b=c then a=c
Term
Theorem
Definition
A statement that follows as a result of other true statements. All theorems must be proven in order to be considered a theorem.
Term
Right angle congruence theorem
Definition
All right angles are congruent
Term
Congruent Supplements Theorem
Definition
If two angles are supplementary to the same angle, then they are congruent to each other.
Term
Congruent complements theorem
Definition
If 2 angles are complementary to the same angle, then they are congruent to each other.
Term
Linear pair postulate
Definition
If 2 angles form a linear pair, then they are supplementary.
Term
Verticle angles theorem
Definition
If two angles are vertical angles, then they are congruent.
Term
Parallel lines
Definition
Coplanar lines that never intersect
Term
Skew lines
Definition
Lines in different planes that never intersect
Term
Parallel planes
Definition
Planes that don't intersect
Term
Parallel postulate
Definition
If there is a line and a point not on a line, then there is one line through the point parallel to the given line.
Term
Perpendicular postulate
Definition
If there is a line and a point not on the line, then thereis one line through the point perpendicular to the given line.
Term
Theorem 3.1
Definition
If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Term
Theorem 3.2
Definition
If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
Term
Theorem 3.3
Definition
If two lines are perpendicular, then they intersect to form four right angles.
Term
Transversal
Definition
A line that intersects coplanar lines in two or more different points.
Term
Corresponding Angles postulate
Definition
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Term
Alternate interior angles theorem
Definition
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent
Term
Consecutive Interior angles theorem
Definition
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
Term
Alternate exterior angles theorem
Definition
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
Term
Perpendicular to parallels theorem
Definition
If a transversal is perpendicular to one of two paralllel lines, then it is perpendicular to the other.
Term
Corresponding angles converse postulate
Definition
If two lnes are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Term
Alternate interior angles converse theorem
Definition
If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.
Term
Consecutive interior angles converse theorem
Definition
If two lines are cut by a transversal so that consecutive ihnterior angles are supplementary , then the lnes are parallel.
Term
Alternate exterior angles converse theorem
Definition
If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.
Term
Transitivity of Parallels theorem
Definition
If two lines are parallel to the same line, then they are parallel to each other.
Term
Two perpendiculars Theorem
Definition
In a plane, if two lines are perpendicular to the same line, then they are parallel to each other.
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