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81 Cards in this Set
- Front
- Back
- 3rd side (hint)
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Undefined Figures
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point, line and plane
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3
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Point
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Undefined figure. Represented by a capitol, printed letter (A, B, C).
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definition
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Line
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Undefined figure. Common definition: a set of infinite points in a straight pattern. Represented by naming any two points on it with a line over it OR a lowercase cursive letter.
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definition
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Plane
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A flat figure with infinite length and width but has no figure. Drawn as a parallelogram. Represented by naming at least 3 points in clock or counter clockwise patter. Named with a capitol cursive letter.
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definition
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Ray
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A piece of a line with one endpoint. Represented by naming endpoint first and then any other point on it. A ray must be drawn on the top of the named letters and it must be pointing to the right.
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definition
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Segment
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A piece of a line with two end points. Represented by naming both points in the segment. Must have a line segment on top of the represented letters.
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definition
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Angles
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The union of two rays with the same endpoint (vertex)
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definition
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Figure
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a set of points
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definition
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Collinear
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on the same line
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definition
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Counter Example
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a statement that is not always true.
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definition
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Coplanar
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on the same plane
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definition
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Space
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the set of all points
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definition
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Congruent
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“is congruent to”. Same size and same shape. Tic/hash marks show that the two figures are the same size and shape
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definition
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Midpoint
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a point in the middle. A point that divides a segment into two equal parts
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definition
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Segment bisector
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a ray/line/plane/segment that contains the midpoint.
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definition
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Postulate
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a statement without proof (doesn’t need proof)
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definition
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Theorem
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a theory/statement that has been proven true.
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definition
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Property
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rules of math
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definition
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Definition
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meaning
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definition
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Between
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a point is between two other points if it is on the segment connecting those two points.
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definition
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Good Diagram
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an illustration that shows nothing more and nothing less than the given information.
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definition
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Acute
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an angle who’s measure is less than 90 degrees.
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definition
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Obtuse
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an angle who’s measure is between 90 and 180 degrees.
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definition
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Right
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an angle who’s measure is exactly 90 degrees.
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definition
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Straight Angle
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angles whose measure is exactly 180 degrees.
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definition
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Complimentary Angles
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a measure of two angles whose sum adds up to 90 degrees.
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definition
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Supplementary Angles
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a measure of two angles whose sum adds up to 180 degrees.
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definition
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Adjacent Angles
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two angles with the same vertex and a common side between them.
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definition
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Vertical Angles
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two angles with the same vertex formed by opposite rays.
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definition
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Linear Pair
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two adjacent angles whose non-common sides are opposite rays
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definition
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Inductive
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based on a conclusion that was based on observation.
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definition
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Deductive
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decision based on what you already know.
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definition
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Coordinate
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a number that goes along with a point.
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definition
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Formula
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a theorem that involves numbers
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definition
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Points Postulate
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Space contains at least 4 noncoplanar, noncollinear points. A plane contains at least 3 noncollinear points. A line contains at least 2 points.
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Line Postulate
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Two points are contained in one and only one line.
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Plane Postulate
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Three noncollinear points are contained in one and only one plane.
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Flat Plane Postulate
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If two points are contained in a plane, the line through them is contained in the same plane.
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Plane Intersection Postulate
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If two planes intersect, they intersect a line.
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Ruler Postulate
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For every pair of points, there is a unique positive real number called the distance between them.
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Segment Construction Postulate
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On any ray, there is exactly one point at a given distance from the endpoint of a ray.
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Segment Addition Postulate
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If P is between A and B, then AP+BP=AB.
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Midpoint Postulate
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A segment has exactly one midpoint.
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Protractor Postulate
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The measure of an anhle is a positive real number.
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Angle Construction Postulate
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Let H1 be a half plane with edge ray PA. There is exactly one ray, ray PB with B, in H1 such that angle APB has a given measure.
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Segment Construction Postulate with angles.
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Angle Addition Postulate
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If B is in the interior of angle APC then the mAPB+mBPC=mAPC.
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Angle Bisector Postulate
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An angle has exactly one bisector.
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Supplement Postulate
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The angles in a linear pair are supplementary.
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theorem
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Two intersecting lines are always coplanar.
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theorem
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A line and a point on the line are always on the same plane.
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theorem
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No matter what, the measure of an angle is always 180 degrees.
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theorem
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D = l C1 – C2l
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theorem
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Midpoint = C1 + C2/2
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theorem
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Vertical angles are congruent
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theorem
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All right angles are congruent
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Perpendicular Lines
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Two lines that intersect to form two right angles.
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definition
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Parallel Lines
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Coplanar lines that never intersect
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definition
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theorem
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Two intersecting lines intersect at one and only one point
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Reflexive Property
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a=a
AB=AB RS+CD=RS+CD |
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Symmetric Property
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If a=b, then b=a. If RS=CD, then CD=RS.
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Transitive Property
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If a=b and b=c, then a=c.
If AB=CD and CD=8, then AB=8. |
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Substitution Property
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If a=b and a=c then b=c.
- If two things are equal, whenever you see one, you may substitute. - If two things are equal to the same thing, then they're equal to eachother. |
IMPORTANT TO KNOW
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Distributed Property
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a (b+c)= ab+ac
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Trichotomy Property
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If a and b are reflexive then a<b or a=b or a>b.
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Addition Property
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If a=b and c=d,
a+c=b+d |
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Subtraction Property
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If a=b and c=d,
a-c=b-d |
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Multiplication Property
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If a=b and c=d,
ac=bd |
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Division Property
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If a=b and c=d,
a/c=b/d |
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theorem
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Congruence of segments and angles are reflexive, symmetric, and transitive.
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theorem
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Supplements of congruent angles are congruent.
Compliments of congruent angles are congruent. |
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theorem
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Supplemens of the same angle are congruent.
Compliments of the same angle are congruent. |
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Conditional Statements
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If, then statements.
If_____(hypothesis) then ________(conclusion) |
definition
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Converse Statements
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a conditional statement formed by swapping the hypothesis and conclusion.
q->p (if q then p) |
definition
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Bi-conditional Statements
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a conditional statement combined with its converse.
p<->q |
definition
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iff
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if and only if
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definition
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Negation
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the opposite (~)
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definition
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Inverse Statements
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a conditional statement formed by negating both the hypothesis and the conclusion.
~p->~q |
definition
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Contrapositive Statements
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the negation of a converse statement.
~q->~p |
definition
C~C |
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Midpoint theorem
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If B is the midpoint of segment AC, then AB=1/2AC.
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do not say midpoint theorem in proofs, simply say "midpoint"
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theorem
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If the angles of a linear pair are congruent, then the lines containing their sides are perpendicular.
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Angle Bisector Theorem
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If ray BD bisects angle ABC, then anlge ABD= 1/2ABC.
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state as "angle bisector" in proofs
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