Angle Addition Postulate If B is in the interior of <AOC then m<AOB + m<BOC = m<AOC
Alternative Interior Angles The angles formed when 2 lines are cut by a transversal that are in between the 2 lines and on opposite sides of the transversal Midpoint Formula "M = ((x<span style=""font-size:xx-small"">1</span> + x<span style=""font-size:xx-small"">2</span>)/2, y<span style=""font-size:xx-small"">1</span> + y<span style=""font-size:xx-small"">2</span>)/2)"
Segment bisector "A line ray or segment that goes through a segment at it's midpoint"
Inductive Reasoning Using patterns to make a generalization called a conjecture Defined terms Terms that are defined using undefined terms
Undefined termsTerms that we give definitions to, so we can use them to define other terms. The undefined terms of geometry are point, line, and plane.
SlopeThe rate of change in a line, or how steep it is
Supplementary Angles Angles that sum to 180°
Conditional Statement "A statement that can be written as and if then statement. The ""if"" clause is the hypothesis and the ""then"" clause is the conclusion.&nbsp;"
Converse of a conditional statement Formed by flipping the hypothesis and the conclusion. Ex. If p then q, if q then p.
Inverse of a conditional statement Formed by negating the hypothesis and conclusion. Ex. If not p then q, if p then not q
Contrapositive of a conditional statement Formed by negating the hypothesis and conclusion and flipping the hypothesis. Ex. If p then not q, if q then not p.
Alternative Exterior AnglesNon adjacent angles on opposite sides of the transversal and on outside the lines.
Alternative Exterior Angles Theorem If 2 parallel lines are cut by a transversal, then the alternative exterior angles are congruent.
The Law of Syllogism If p-&gt;q and q-&gt;r are true then p-&gt;r.
Law of Detachment If given a true conditional and another true hypothesis, then you can create a true conditional. Ex. If someone buys a ticket to a movie then they can see a movie. Abdullah bought a ticket to The Lion of Ain Jaloot, Abdullah can see the The Lion of Ain Jaloot
Opposite Rays Two rays that share an endpoint and go in opposite directions along the same line.
Perpendicular PostulateIf given a line and a point, then there is exactly one line through the point that is perpendicular to the line.
Perpendicular Transversal TheoremIf a transversal is perpendicular to one of 2 parallel lines, then it is also perpendicular to the other line
Corresponding AnglesA pair of non-adjacent angles such that the angles are on the same side of the transversal and one is outside the 2 lines and one is in-between the 2 lines.
Congruent Complements TheoremIf 2 angles are complementary to the same angle or 2 congruent angles, then the 2 angles are congruent.
Line SegmentA section of a line with 2 endpoints, containing all the points along the line between the 2 points. An undefined term.
Angle BisectorA ray that divides an angle into 2 congruent angles
Same Side Interior Angles TheoremIf 2 parallel lines are cut by a transversal, then the same side interior angles are supplementary.
Perpendicular Slopes Theorem"If 2 non-vertical lines are perpendicular, then the slopes' product is -1."
Converse of the Same Side Interior Angles TheoremIf 2 lines are cut by a transversal such that the same side interior angles are supplementary, then the lines are parallel.
Parallel Lines Theorem2 non-vertical lines are parallel if and only if they have the same slope.
Vertical LinesUndefined slopes, are perpendicular to horizontal lines and parallel to other vertical lines.
Congruent Supplements TheoremIf 2 angles are supplementary to the same angle or 2 congruent angles, then they are congruent angles.
Right Angles TheoremIf 2 angles are right angles, then they are congruent.
Vertical AnglesNon-adjacent angles formed by 2 intersecting lines.
Vertical Angles TheoremIf 2 angles are vertical angles, then they are congruent
Subsitution PropertyIf A + 5 = 10 and A = B, then B + 5 = 10
Linear Pair Angles"Adjacent angles who's unshared sides form opposite rays."
Perpendicular LinesLines that intersect to form a right angle
Perpendicular Lines TheoremIf 2 lines are perpendicular, then they form 4 right angles.
Reflexive Property of Congruence"<div style=""text-align: center;"">An angle, shape, or line is always congruent to itself. &lt;A is congruent to &lt;A</div>"
Reflexive Property of EqualityThe length, measure, or area of a line, angle, or shape is equal to itself. M&lt;A = M&lt;A
Symmetric Property of CongruenceIf &lt;A is congruent to &lt;B, then &lt;B is congruent to &lt;A
Ruler PostulateFor pairs of points:<br>Points can be matched with numbers on a number line<br>There is one unique number for the distance between 2 points and is |distance|
Congruent SegmentsSegments with the same length or measure
Created using a compass and a straight edge, never measured with a ruler or protractor (unless to check.)Constructions
2 Column ProofA method of proving a statement using a 2 column table. One column is statements, the other is reasons, and each is numbered.
Flow ProofA method of logically proving a statement using ovals/boxes connected by arrows.
Paragraph ProofComprehensive paragraphs that explain the process of a proof
Translation"A rigid motion transformation where the figure's shape and size remains the same, but the position changes."
Rigid Motion Transformation"A transformation where an object's size and shape remain the same"
VectorShows the direction of a horizontal and/or vertical change
ReflectionA rigid motion transformation where a figure undergoes a change in position that creates a mirror image on the opposite side of the line of reflection
Function Notation (Tranformations)(x,y)&nbsp; --&gt; (Change in X, Change in Y)
Vector Notation&lt;Change in X, Change in Y&gt;
PostulateA statement accepted without proof or reasoning
TheoremA statement that must be proven using deductive reasoning
Congruent AnglesAngles with the same measure
Protractor Postulate"<ul><li>Angles can be measured from 0-180 degrees</li><li>There is a 1:1 with the rays of an angle and the numbers on a protractor, and the measure is equal to |difference (of the rays' matching numbers)|</li></ul>"
Straight AngleAn angle with a measure of 180
ConjectureA generalization created by using inductive reasoning
False Conditonal<ul><li>Has a true hypothesis but a false conclusion</li><li>Requires only one counter-example to be proven false</li></ul><br>
Biconditional Statement"<b><div><table><tbody><tr><td><div><span style=""font-weight: 400; color: rgb(255, 255, 255);"">A conditional statement that uses if and only if and is formed by combining the converse and conditional. In order for a biconditional to be true the conditional and converse must be true. Iff can be used instead of if and only if.</span></div></td></tr></tbody></table></div></b>"
Transitive Property of EqualityIf AB = BC, and BC = CD, then AB = CD
Transitive Property of CongruenceIf AB is congruent to BC, and BC is congruent to CD, then AB is congruent to CD.
Line of Reflection<ul><li>The line a reflected image is reflected across</li><li>Has an equal distance between each pre-image and its corresponding image point</li><li>Is the perpendicular bisector of the line segment between pre-image and image points</li></ul>
RotationA rigid motion transformation that moves a fihure counterclockwise or clockwise about a center of rotation
Center of RotationThe point a rotation occurs around
Degree of a RotationThe amount a figure rotates
Direction of RotationEither clockwise or counterclockwise
Function rule for 90 degree counterclockwise rotations(x,y) --&gt; (-y,x)
Function rule for 180 degree rotations(x,y) --&gt; (-x,-y)
Function rule for 90 degree clockwise rotations(x,y) --&gt; (y,-x)
Function Rule for a Reflection Over y = x(x,y) -&gt; (y,x)
Triangle Sum TheoremThe measures of the 3interior angles of a trianlge sum to 180 degrees
Exterior Angle Theorem (Triangles)The sum of the measures of the 2 remote interior angles of a triangle are equal to the measure of a given exterior angle
Interior Angle of a TriangleThe angles on the inside of a triangle
Exterior Angle of a TriangleThe angle formed by the extension of a side of the triangle and a preexisting side