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134 Cards in this Set
- Front
- Back
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Collinear points
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points on the same line
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Coplanar
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lines (or other figures) on the same plane
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Parallel Lines
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2+ coplanar lines that never intersect
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Parallel Planes
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2+ planes that never intersect
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Skew Lines
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2+ non-coplanar lines that never intersect
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Line Segment
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made up of 2 points called endpoints of the segment and all the collinear points between them
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Congruent Segments
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segments of equal length
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Ray
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part of a line with 1 endpoint
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Intersection
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where 2+ figures have 1+ points in common
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Postulate
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a rule that is accepted as true without proof
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Theorem
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something that can be proven using postulates or other proven theorems
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Ruler Postulate
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AB = lx1-x2l or x2-x1
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Segment Addition Postulate
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If B is between A and C, then AB + BC = AC
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Angle
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consists of 2 different rays with the same endpoint
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Vertex
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the endpoint in the middle of an angle
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Side (angles)
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the seperate rays of an angle
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Protractor
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a semi-circular tool that measures angles in degrees
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Angle Addition Postulate
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If P is in the interior of <RST, then the measure of <RST is equal to the sum of the measures of <RSP and <PST
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Congruent Angles
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2 angles that mave the same measure
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Angle Bisector
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a ray that divides an angle into 2 congruent angles
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Midpoint
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a point that divides a segment into 2 congruent segments
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Counterexample
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an example to disprove
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Adjacent angles
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angles that share a vertex and a side (ray) and have no common interior points
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Linear Pair
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adjacent angles whose sum is 180 degrees
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Vertical Angles
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Angles that share a vertex and no sides and are conruent
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Complementary Angles
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2 angles whose sum in 90 degrees, sometimes adjacent
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Supplementary Angles
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2 angles that sum to 180 degrees, sometimes adjacent
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Polygon
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closed plane figure with 3+ sides, each of which intersects exactly 2 sides, one t each endpoint, so that no two sides with a common endpoint are collinear
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Triangle
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3-sided polygon
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Quadrilateral
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4-sided polygon
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Pentagon
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5-sided polygon
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Hexagon
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6-sided polygon
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Heptagon
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7-sided polygon
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Octagon
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8-sided polygon
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Nonagon
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9-sided polygon
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Decagon
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10-sided polygon
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Dodecagon
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12-sided polygon
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Pentadecagon
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15-sided polygon
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n-Gon
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a polygon with n sides
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Congruent Polygons
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polyons with congruent sides and congruent angles
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Perimeter
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distance around a figure (units)
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Circumference
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distance around a circle (units)
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Area
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amount of surface covered on a figure (squared units)
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Inductive Reasoning
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looking for patterns and trends; not absolute; specific to general
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Conjecture
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used to generalize information after analyzing data
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Deductive Reasoning
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using facts, knowledge, and properties; absolute; general to specific
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Conditional Statement
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type of logical statement that has two parts, a hypothesis and a conclusion (format of writing conjectures); p-->q
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Negation
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the opposite of a statement; ~p
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Converse
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statement formed by exchanging the hypothesis and conclusion of a conditional statement; not always true; q-->p
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Inverse
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statement formed by negating the hypothesis and conclusion of a conditional; ~p-->~q
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Contrapositive
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equivatlent statement formed by negating the hypothesis and conclusion of the converse of a conditional statement; ~q-->~p
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Equivalent Statements
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when 2 statements are both true or both false
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Biconditional Statement
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statement containing the phrase "if and only if"; can be used when a conditional and its converse are both true
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Law of Detachment (Modus Ponens)
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if the the hypothesis of a true conditional statement is true, them the conclusion is also true
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Modus Tollens
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If the conclusion of a true conditional statement is false, then the hypothesis is also false
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Law of Syllogism
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If p-->q and q-->r, then p-->r
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Through and 2 points there exists _______ line(s).
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exactly one
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a line contains _________ point(s).
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at least 2
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if 2 lines intersect, then their intersection is _________.
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a point
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through any 3 non-collinear points there exists ___________ plane(s).
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exactly one
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a plane contains ____________ non-collinear point(s).
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at least 3
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if 2 points lie in a plain, then the line containing the 2 points is where?
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in the plane
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if 2 planes intersect, then their intersection is ________.
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a line
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Addition Property
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If a=b, then a+c=b+c
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Subtraction Property
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If a=b, then a-c=b-c
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Multiplication Property
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If a=b. then ac=bc
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Division Property
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If a=b, then a/c=a/b
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Distributive Property
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a(b+c)=ab+ac
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Substitution Property
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If a=b, then b can be substituted for a (or vice versa) in an equation or expression
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Reflexive Property
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AB=AB
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Symmetric Property
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If AB = CD, then CD = AB
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Transitive Property
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If a=b and b=c, then a=c
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Theorem
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statement that can be proven
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Right Angles Congruence Theorem
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If 2 angles are right angles, then they are congruent (All right angles are congruent).
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Congruent Complements Theorem
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If 2 angles are complementary/supplementary to the same angle, then they are congruent.
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Linear Pair Postulate
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If 2 angles are a linear pair, then they sum to 180 degrees (they are supplementary)
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Parallel Postulate
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If there is a line and a point not on the line, then exactly one line can go through the point parallel to the first line
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Perpendicular Postulate
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If there is a line and a point not on the line, then exactly one line can go through the point perpendicular to the first line
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Transversal
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line that intersects two or more coplanar lines at different points
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Alternate Interior Angles
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Angles in the interior region on opposite sides of a transversal
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Alternate Exterior Angles
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Angles on opposite sides of the transversal in the exterior region
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Same-Side Interior Angles
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Angles on the same side of the transersal in the interior region
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Same-Side Exterior Angles
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Angles on the same side of the transversal in the exterior region
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Corresponding Angles
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2 angles, one in the interior region and 1 in the exterior region, on the same side of the transversal
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Corresponding Angles Postulate
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If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent; converse also true
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Same-Side Interior Angles Theorem
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If 2 parallel lines are cut by a transversal, then same-side interior angles are supplementary; converse also true
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Alternate Exterior Angles Congruence Theorem
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If 2 parallel lines are cut by a transversal, then alternate exterior angles are congruent; converse also true
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Same-Side Exterior Angles Theorem
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If 2 parallel lines are cut by a transversal, then same-side exterior angles are supplementary; converse also true
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Anternate Interior Angles Theorem
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If 2 parallel lines are cut by a transversal, then alternate inerior angles are congruent; converse also true
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Transitive Property of Parallel Lines
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If p//q and q//r, then p//r
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Slope
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ratio of the vertical change to horizontal change between any two points on a line
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m=0
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slope of a horizontal line
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m=undefined
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slope of a vertical line
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Slope-Intercept Form
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y=mx+b
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Standard Form
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Ax+By=C
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Point-Slope Form
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y-y1=m(x-x1)
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Dual Perpendicular Theorem
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If 2 limes are perpendicular to the same line, then they are parallel to each other
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Scalene
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Triangle with no congruent sides
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Isosceles
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Triangle with at least 2 congruent sides
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Equilateral
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Triangle with all sides congruent; also equiangular
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Acute
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Triangle in which all angle measures are <90 degrees
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Obtuse
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Triangle in which one angle is >90 degrees and the other 2 are acute
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Right
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Triangle in which one angle measures 90 degrees and the other 2 are acute; legs are sometimes congruent
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Exterior Angle Theorem
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If an angle is an exterior angle, then it is = to the sum of the measures of the 2 non-adjacent interior angles
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Corollary
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statement that can be proven easily using a theorem
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SSS Congruence Postulate
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If 3 sides of a trangle are congruent to 3 sides of another triangle, then the triangles are congruents
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HL Congruence Theorem
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If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse of leg of another right triangle, then the 2 triangles are congruent
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Included angle
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angle whose vertex is shared by the given sides of a figure
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SAS Congruence
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If 2 sides and the included angle of a trangle are congruent to 2 sides and the included angle of another triangle, then the 2 triangles are congruent
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ASA Congruence
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If 2 angles and the included side of a triangle are congruent to 2 angles and the included side of another triangle, then the 2 triangles are congruent
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AAS Congruence
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If 2 angles and a non-included side of a triangle are congruent to 2 angles and the non-included side of another triangle, then the 2 triangles are congruent
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CPCTC
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Corresponding Parts of Congruent Triangles are Congruent
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Base Angles Theorem
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If 2 sides of a triangle are congruent, then the angles opposite those sides are conguent
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Converse of Base Angles Theorem
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If 2 angles in a triangle are congruent, then the sides opposite those angles are congruent
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Midsegment
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segment that onnects the midpoints of 2 sides of a triangle; 3 divide a triangle into 4 congruent triangles
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Midsegment Theorem
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If a segment connects the midpoints of 2 sides of a triangle, then it s parallel to the 2rd side and is 1/2 the lingth of the 3rd side
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Equidistant
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the same distance from one figure as from another figure
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Segment Bisector
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line/ray/plane/segment that passes through the midpoint of a segment
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Perpendicular Bisector
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line/ray/plane/segment that passes through the midpoint of a segment and is perpendicular to the segment
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Perpendicular Bisector Theorem
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If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment; converse also true
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Concurrent
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when 3+ lines/rays/segments intersect at a common point
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Point of Concurrency
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common point where 3+ lines/rays/segments intersect
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Circumcenter
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Point of concurrency of perpendicular bisectors
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Angle Bisector
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ray that divides an angle into 2 congruent adjacent angles
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Incenter
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Point of concurrency for the 3 angle bisectors
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Angle Bisector Theorem
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If a point is on the bisector of an angle then it is equidistant from the 2 sides of the angle; converse also true
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Median
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segment connecting the vertex of a triangle to the midpoint of the opposite side
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Centroid
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point of concurrency for 3 medians of a triangle
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Median Theorem
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If a line segment connects a triangle's vertex to the midpoint of the opposite side, then the centroid is 2/3 of the distance from the vertex to the midpoint
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Altitude
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a perpendicular segment from a vertex of a triangle to the opposite side; used to find height of a triangle
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Orthocenter
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point of concurrency for the 3 altitudes of a triangle
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Triangle Inequality Theorem
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If 3 segments form a triangle, then the sum of any 2 segments must be greater than the 3rd
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Angle Inequalities in a Triangle
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- The longest side is opposite the largest angle
- The shorthest side is opposite the smallest angle |
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Hinge Theorem
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If 2 sides of a triangle are congruent to 2 sides of another triangle, and the included angle in the 1st triangle is larger than that of the 2nd triangle, then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle
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