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96 Cards in this Set
- Front
- Back
Point
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A location
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Line
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Made up of points, has no thickness or width; continues in both directions infinitely
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Plane
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Flat surface made up of points, has no depth or thickness; extends infinitely
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Undefined terms
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Can only be defined by descriptions
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Collinear
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Points on the same line
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Coplanar
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Points or lines on the same plan
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Space
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A boundless, 3-D set of points, cotains all lines, points, and planes
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Line segment
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Part of a line with two definte endpoints, named by those endpoints
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Congruent segment
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2 line segments have the same measurement
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Segment bisector
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a line, plane, or segment that intersects a segment at its midpoint
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Ray
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part of a line, one endpoint and one infinite end; named by 2 points with the endpoint listed 1st
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Oppisite rays
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Any point on a line forms a pair of oppisite rays
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Angles
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Made up of two sides (lines, rays, segment) and a vertex
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Angle bisector
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A line, segment, or ray that divides an angle into two congruent angles
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Adjacent angles
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Two angles sharing a vertex and a side (rays, line segments, lines)
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Vertical angles
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Two angles across from each other when 2 lines intersect; VERTICAL ANGLES ARE ALWAYS CONGRUENT!
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Supplementary angles
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Two angles whose measurments add to 180 degrees; DO NOT have to be adjacent!
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Linear pair (Linear angles)
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2 adjacent supplementary angles
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Complementary angles
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2 angles whose measurments add to 90 degrees; DO NOT have to be adjacent!
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Perpendicular lines/segments/rays
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2 lines/segments/rays that intersect to form 90 degree angles
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Inductive reasoning
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Making predictions based on patterns
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Conjectures
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An educated guess based on known information
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Counterexample
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A false example; anything that disproves a conjecture
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Statement
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Any sentence that is either true or false, but not both (represented by a letter; most common...p,q,r)
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Negation
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giving a statement the oppisite meaning and truth value
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Compound statements
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2 or more statements joined by either"and" or "or"
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Conditional statement
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If...Then...statement; the "then" depends on the "if"
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Logically equivalent
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When statements have the same truth value
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Deductive reasoning
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Making predictions based on facts
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Law of detachment
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If p---q is true, and p is true, then q is true.
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Law of syllogism
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If p---q and q---r are both true, then p---r is also true
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Proof
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A logical argument in which a statement you make is supported by reasons
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Paragraph proof
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Informal proof, not very structured, writing out your thought process
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Midpoint theorem
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If M is the mdpt of AB, then AM is congruent to MB
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2 column proof
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Very organized; with 2 columns; statements and reasons
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Parallel lines
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Coplanar lines that do not intersect
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Parallel planes
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planes that never intersect
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Skew lines
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non-coplanar, non-parallel lines that do not intersect
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transversal
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A line that intersects 2 or omre lines in the same plane
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Alternate interior angles
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Interior angles on oppisite sides of the transversal and oppisite sides of interior
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Alternate exterior angles
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exterior angles on oppisite sides of the transversal and oppisite sides of the exterior
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Consecutive interior angles
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Interior angles on the same side of the transversal
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Corresponding angles
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Angles in the same position at an intersection
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Postulate
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A statement about geometry that is accepted as true
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Theorem
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A statement about geometry that has been proven true
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Corresponding angle postulate
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* If 2 parellel lines are cut by a transversal, then each pair of corresponding angles are congruent
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Alternate interior angles theorem
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If 2 parellel lines are cut by a transversal, then alt. int. angles are congruent
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Consecutive interior angles theorem
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if 2 parellel lines are cut by a transversal, then consec. int. angles are supplementery
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Slope
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A ratio of lines vertical (rise) over its horizontal (run)
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Postulate about parellel lines about slopes
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If 2 lines are parellel, then their slopes are congruent
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Postulate about perpindicular lines with slope
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If 2 lines are perpendicular, then their slopes oppisite recipricols
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Congruent triangles
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2 or more triangles with exactly the same shape annd size
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CPCTC
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Corresponding Parts of Congruent Triangles are Congruent
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Side-side-side (SSS)
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If the sides of one angle are congruent to the sides of another triangle, then they are congruent
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Side-angle-side (SAS)
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If two sides and the included angle os a triangle is congr. to the corresponding 2 sides and included angle, then the 2 triangles are congr.
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Angle-side- angle (ASA)
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If two angles and the included side of one triangle is congr. to to angles and the included side of another triange, then the 2 triangles are congr.
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Angle-angle-side (AAS)
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If two angles and a non-included side of one angle is congr. tot he corresponding 2 angles and non-included side, then the 2 triangles are congr.
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Flow proof
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Organizes a series of statements in a logical order; each statement is written in a box with the reason written below the box
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Hypotenuse-Leg Congruence
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If the hypotenuse and one of your legs are congr., then the 2 triangles are congr.
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Ratio
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a comparison of two numbers
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Porportion
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An equation stating that 2 ratios are equal
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Scale factor
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Ratio of corresponding sides of similar figures
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Similar figure
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all corresponding angles are congr., and all crresponding sides have the same scale factor
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Angle-angle similarity (AA~)
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If two angles of one triangle are congr. to two angles of another triangle, then the 2 triangles are similar
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Side-side-side similarity (SSS~)
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If the corresponding sides of 2 triangles have the same sclae factor, then they are similar
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Parallel line theorems (4)
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-If alt int angles are congr, then the lines are parallel.
-If alt ext angles are congr, then the lines are parallel. -If consec int angles are supplementary, then the lines are parallel. -If 2 lines are perpendicular to the same line, then those lines are parallel. |
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3rd angle theorem
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If 2 angles of one triangle are cong. to 2 angles of another triangle, then the 3rd angles are congr.
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Exterior angles theorem
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The ext angle of a triangle is = to the sum of 2 remote int angles.
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Isosceles triangle theorem
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If a triangle is isosceles, then the angles opposite the congr. sides are congr.
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SAS inequality theorem
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If 2 sides of a triangle are congr to 2 sides of another triangle, and the included angle in one triangle is greater then the included angle of another triangle, thenthe third side of the 1st triangle is longer then the 3rd side of the other triangle
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SSS inequality theorem
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If 2 sides of a triangle are congruent to 2 sides of another triangle, and the 3rd side of one triangle is greater then the 3rd side of another triangle, then the angle between the pair of congr. sides of the first triangle is greater then the corresp. angle in the other triangle
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Triangle Midsegment Theorem
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A Triangle Midsegment is:
- parallel to the 3rd side a segment bisector of the sides it intersects -its length is half of the 3rd side |
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Corollary
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A statement that can easily be proven by a theorem
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Corollary about parallel lines and transversals
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If 3 or more parallel lines are intersected by transvesals, then they cutt of the transversals porportionally
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Porportional Perimeters Theorem
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If two triangles are similar, then their peremiters have the same scale factor
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Theorem about altitude
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If 2 triangles are similar, then their corresponding altitudes are also similar
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Theorem about corresponding angle bisectors
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If 2 triangles are similar, then their corresponding angle bisectors are similar
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Theorem about corresponding medians
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if 2 triangles are similar, then their corresponding medians are similar
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Angle Bisector Theorem
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If an angle bisector in a triangle seperates the oppisite side into segments, then they have the same scale factor as the corresponding sides
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Theorem about altitude and geometric mean
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the altitude drawn to the hypotenuse of a rigth triangle is the geometric mean of the 2 pieces of the hypotenuse
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Theorem about hypotenuse and geometric mean
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each leg of a right triangle id the geometric mean of the whole hypotenuse and the pieceof the hypotenuse closest to the leg
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Converse
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switch the "if" and "then"
q---p |
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Inverse
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Negate the "if" and "then"
~p---~q |
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Contrapositive
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Switch teh "if" and "then" and negate the "if" and "then"
~q---~p |
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Polygon
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A closed figure whose sides are all segments
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Triangle
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3
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Quadrulateral
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4
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Pentagon
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5
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Hexagon
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6
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Heptagon
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7
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Octogon
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8
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Nonagon
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9
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Decagon
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10
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Dodecagon
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12
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N-gon
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N
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Diagonal
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(of a polygon) is a segment that connescts any 2 nonconsecutive vertices
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