| A | B |
|---|
| Conditional statement | Has two parts, a hypothesis and a conclusion. |
| Converse conditional statement | A conditional statement formed by switching the hypothesis and conclusion |
| Equivalent statements | When two statements are both true or both false |
| p->q | Symbolic Notation of Original Conditional Statment |
| q->p | Symbolic Notation of the Converse Statement |
| Biconditional Statement | A conditional statement that contains the phrase “if and only if.” |
| Addition Property | If a = b, then a + c = b + c |
| Subtraction Property | If a = b, then a - c = b - c |
| Multiplication Property | If a = b, then ac = bc |
| Division Property | If a = b and c not equal to 0, then a ÷ c = b ÷ c |
| Reflexive Property of Equality | For any real number a = a |
| Symmetric Property | If a = b, then b = a |
| Transitive Property | If a = b and b = c, then b = c |
| Substitution Property | If a = b then a can be substituted for b in any equation or expression |
| Theorem | A true statement that follows as a result of other true statements |
| Two-column proof | Numbered statements and reasons that show the logical order of an argument. |
| Congruent Supplements Theorem | If two angles are supplements of congruent angles, then the two angles are congruent |
| Congruent Complements Theorem | If two angles are complements of congruent angles, then the two angles are congruent. |
| Linear Pair Postulate | If two angles form a linear pair, then they are supplementary. |
| Vertical Angles Theorem | Vertical angles are congruent. |
| Overlapping Angles Theorem | Given <AOD with points B and C in its interior: If m<AOB=m<COD, the m<AOC=M<BOD. |
| A Reflection theorem | Reflection across two parallel lines is equivalent to a translation of twice the distance between the lines and in a direction perpendicular to the lines. |
| If-Then Transitive Property | Given "If A then B, and if B then C." You can conclude "If A then C" |
| Overlapping Segments Theorem | Given a segment with points A, B, C, and D (in order), then: If AB=CD, then AC=BD. Conversely, "If AC=BD, then AB=CD". |
| Segment Congruence Postulate | If two segments hae the same length, then they are congruent. |
| Segment Congruence Postulate | If two segments are congruent, then they have the same length. |
| Angle Congruence Postulate | If two angles have the same measure, then they are congruent |
| Angle Congruence Postulate | If two angles are congruent, then they have the same measure |
| Angle Addition Postulate | If point D is in the interior of <ABC, then m<ABD+m<DBC=m<ABC |
| Segment | A part of a line that begins at one point and ends at another |
| Ray | A part of a line that starts at a point and extends indefinitely in one direction. |
| Angle | A figure formed by two rays with a common endpoint. |
| Vertex of an angle | Common endpoint of an angle |
| Sides of an angle | The rays of an angle |
| The intersection of two lines | A point |
| The intersection of two planes | A line |
| Through any two points... | There is exactly one line |
| Through any three noncollinear points... | There is exactly one plane |
| Segment Addition Postulate | If point R is between P and Q on a line, then PR+RQ=PQ |
| Complementary Angles | Two angles whose measures have a sum of 90 degrees |
| Supplementary Angles | Two angles whose measures have a sum of 180 degrees |
| Right Angle | An angle whose measure is 90 degrees |
| Acute Angle | An angle whose measure is less than 90 degrees |
| Obtuse Angle | An angle whos measure is greater than 90 degrees and less than 180 degrees |
| Perpendicular lines | Two lines that intersect to form a right angle |
| Parallel lines | Two coplanar lines that do not intersecgt |
| Skew lines | Two noncoplanar lines that do not intersect |
| Segment Bisector | A line that divides a segment into two congruent parts |
| Midpoint of a segment | The point where a bisector intersects a segment |
| Perpendicular Bisector | A bisector that is perpendicular to a segment |
| Angle Bisector | A line or ray that divides an angle into two congruent angles |
| Translation | A transformation in which every point of the preimage is moved the same distance in the same direction |
| Rotation | A transformation in which every point of the preimage is moved by the same angle through a circle centered at a given fixed point known as the center of rotation |
| Reflection | A transformation in which every point of the preimage is moved across a line known as the mirror line so that the mirror is the perpendicular bisector of the segment connecting the point and its image. |
| Horizontal Translation | H(x,y)->(x+h,y) |
| Vertical Translation | V(x,y)->(x,y+v) |
| Reflection across the x-axis | R(x,y)->(x,-y) |
| Reflection across the y-axis | R(x,y)->(-x,y) |
| 180-degree rotation about the origin | R(x,y)->(-x,-y) |
| Adjacent Angles | Angles in a plane that have their vertex and one side in common but have no interior points in common. |
