Geometry Semester One Final Flashcards
A part of a line consisting of one endpoint and extends forever in one direction
Ray
A point, segment, line, or place that intersects a segment at it’s midpoint cutting the segment into two congruent pieces
Segment bisector
What is the midpoint formula
x+x y+y
M=( —
Segments or angles that have the same measure
Congruent
A part of a line consisting of 2 endpoints and everything between
Line segment
2 rays with a common endpoint extending in opposite directions. They combine to create a line
Opposite rays
Points that are not on the same plane
Noncoplanar
The set of all points it’s boundless and three dimensional
Space
Points that are on the same plane
Coplaner points
Points that are not on the same line
Non-collinear points
Points that are on the same line
Collinear points
A flat surface made of points continue infinitely in on directions
Plane
The set of all points continuing in opposite directions from a given point it has neither size nor shape
Line
A location in space with neither size nor shape
Point
Shape formed by two noncollinear rays with a common endpoint
Angle
Sides of an angle
To noncollinear rays
And angle whose measure is greater than 0° but less than 90°
Acute angle
Angle whose measure is exactly 90°
Right angle
An angle whose measure is greater than 90° but less than 180°
Obtuse angle
And angle whose measure is exactly 180°
Straight angle
A line, Ray, or segment which divides an angle into two congruent angles
Angle bisector
Angles that share a vertex and a common side but do not overlap
Adjacent angle
Two nonadjacent angles formed by intersecting lines
Vertical angle
Two angles with measures that have a sum of 90°
Complementary angles
Two angles with a measure that have the sum of 180°
Supplementary angles
Any two lines, rays or segment whose intersection creates90° angles
Perpendicular
The intersection of two lines
.
The intersection of two planes
Line
The common endpoint of the rays in an angle
For tax
The inside of an angle
Interior
The outside of an angle
Exterior
Two adjacent angles whose noncommon sides are opposite rays. They create a straight line
Linear pair
A point, segment, line,place that intersects a segment at its midpoint, cutting the segment into two congruent
Segment bisector
The point halfway between the endpoints of the segment
Mid point
The measure of an angle
Degree
Shape where all of its sides are line segments all of its sides intersect at the endpoints of the segment
Polygon
Where the sides intersect at the endpoints of the segment of a polygon
Vertex of a polygon
A polygon where all sides are equal lateral and all angles are equal angular.
Regular polygon
All sides are congruent
Equilateral
All angles are congruent
Equal angular
A polygon with three sides
Triangle
A polygon with four sides
Quadrilateral
A polygon with five sides
Pentagon
A polygon with six sides
Hexagon
A polygon with seven sides
Heptagon
A polygon with eight sides
Octagon
Polygon with nine sides
Nonagon
A polygon with 10 sides
Decagon
A polygon with 11 sides
Undecagon
A polygon with 12 sides
Dodecagon
A polygon with n sides
N gon
The distance around an object. In a polygon, it is calculated by finding the sum of the sides
Perimeter
The distance around a circle
Circumference
Measures of the number of square units needed to cover the surface of a figure
Area
A guess or hypothesis of what you think might happen next. Not necessarily based on any previous knowledge or information
A conjecture in non-mathematical terms
Using a number of specific examples or patterns to arrive at a conclusion
Inductive reasoning
A conclusion of what happens next based upon patterns or an example noted when using inductive reasoning. may or may not be correct.
Mathematical conjecture
And example that shows how the conclusion or conjecture could be wrong
Counterexample
A sentence that is either True or false
Statement
Truth value
Either true or False
A statement that has the opposite meaning and truth value of the original statement
Negation
Statement symbol
p
Negations symbols
~p
Statements with And
Conjunction
Statements with or
Disjunction
Symbol for conjunction
Symbol for disjunction
V
A statement were two different thoughts are combined
Compound statement
Drawings with intersecting shapes that show common characteristics of different groups
Venn diagram
A method for organizing truth values use of individual statements and compound statements. It shows the results for different combinations of true and false statements.
Truth table
A statement that is written in if then form. Can be true or false
Conditional statement
The part of a conditional statement that follows the word if
Hypothesis
The part of a conditional statement that follows the word then
Conclusion
Formed by switching the hypothesis and the conclusion of a statement
Converse of a statement
Formed by negating the hypothesis and the conclusion of a statement
Inverse of a statement
Formed by negating and exchanging places of the hypothesis and the conclusion ( it is the inverse of the converse)
Contrapositive of a statement
Which two statements will always have the same truth value
Conditional and the contrapositive will always have the same truth value
Uses facts, rules, definitions, or properties to reach logical conclusion
Deductive reasoning
A form of deductive reasoning that is used to draw conclusions from true conditional statements
Law of detachment
Similar to the transitive property of equality. You can use it to determine whether he valid conclusion can be reached from the set of conditional statement
Law of syllogism
A way to organize statements and reasons it is easy to follow format. This is considered a more formal style of proof that a paragraph proof
To column proof
Coplanar lines that do not intersect
Parallel
Planes that do not intersect
Parallel planes
Intersecting lines that form a right angle
Perpendicular
Noncoplanar lines that do not intersect
skew lines
A line intersects two or more coplanar lines at two different points
Transversal
Interior angles that lie on the same side of the transversal
Consecutive interior angles
Nonadjacent exterior angles that lie on alternating sides of the transversal
Alternate exterior angles
Non-adjacent interior angles that lie on the alternating sides of the transversal
Alternate interior angles
Angles that lie on the same position with respect to both the transversal and intersected line
Corresponding angles
Triangle with one right angle
Right triangle
A triangle with one obtuse angle
Obtuse triangle
If triangle with three acute angle
Acute triangle
A triangle with Three congruent angles each angle will be 60°
Equal angular triangle
A triangle with At least two congruent sides
Isosceles triangle
If triangle with no congruent sides
Scalene triangle
Angles formed by one side of a triangle and the extension of another sign
Exterior angles
Angles inside the triangle that are not adjacent to the exterior angle
Remote interior angles
