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96 Cards in this Set

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