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Geometry Mid-Term Vocab Chapters 1-6
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Gravity
Terms in this set (100)
Line Segment
part of a line with two end points
Precision
1. Depends on the smallest available unit of measurement
2. Always going to be within .5 or half of the unit measurement
Collinear
points that lie on the same plane
Coplaner
points that lie on the same plane
Ray
is part of a line that has one endpoint and extends indefinitely in the other direction
Opposite Rays
Share the sam endpoint but extend in opposite directions
Angle
two noncollinear rays that have a common endpoint
Congruent Angles
angles with the same measure
Angle Bisector
line array that splits an angle into two equal angles
Adjacent Angles
two angles that lie in the same plane, have a common vertex, and a common side, but no common interior points
Vertical Angles
two non adjacent angles formed by two intersecting lines
Linear Pair
a pair of adjacent angles whose non-common sides are opposite rays
Complementary Angles
two angles whose measures have a sum on 90 degrees
Supplementary Angles
two angles whose measures have a sum of 180 degrees
Perpendicular Lines
lines that intersect to form 4 right angles
Polygons
a closed figure whose sides are segments and
1. Sides that have a common endpoint are non collinear
2. Adjacent sides intersect only at their endpoints
Concave
lines cross into the interior
Convex
no lines cross into the interior
Regular Polygon
a convex polygon where all sides and angles are congruent
Irregular Polygon
not regular
Perimeter
the sum of the lengths of the sides of a polygon
Conjecture
an educated guess based on known information
Counterexample
a false example that proves the conjecture not to be true
Statement
a sentence that is either true or false, but not both
Truth Value
the truth or falsity of a statement
Negation
changes a statement to the opposite truth value
Compound Statement
combines two or more statements
Conjunction
a compound sentence formed by "AND"
Disjunction
a compound sentence formed by joining statements with "OR"
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
Reflexive Property
for every number a, a=a
Symmetric Property
if a=b, then b=a
Transitive Property
if a=b and b=c, then a=c
Addition and Subtraction Properties
if a=b, then a+c=b+c or a-c=b-c
Multiplication and Division Properties
if a=b, then ac=bc and a/c = b/c (as long as c is not = to 0)
Substitution Property
if a=b, then 'a' may be replaced by 'b' in any equation or expression
Distributive Property
a(b+c) = ab+ac
Postulates
describes fundamental relationships between basic terms in geometry, accepted as TRUE
Postulate 2.1
Through any two points, there is exactly one line
Postulate 2.2
Through any three points not on the same line, there is exactly one plane
Postulate 2.3
A line contains at least two points
Postulate 2.4
A plane contains at least three points not on the same line
Postulate 2.5
If two points lie in a plane, then the entire line containing those points lies in that plane
Postulate 2.6
If two lines intersect, then their intersection is exactly one point
Postulate 2.7
If two planes intersect, then their intersection is a line
Theorem
A statement or conjuncture that is shown to be true
Proof
A logical argument in which each statement you make is supported by a statement that is accepted as true
Midpoint Theorem
If M is the midpoint of line AB, then AB is congruent to MB
Angle Addition Postulate
If R is the is the interior of PQS, then measure of angle PQR + measure of angle RQS = measure of PQS
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of consecutive interior angles are supplementary
Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of alternative exterior angles is congruent
Perpendicular Transversal Theorem
In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other
Slope
m = difference in y-coordinates/difference in x-coordinates
What are special about horizontal lines?
Always have a slope of 0
What are special about vertical lines?
They always have a slope of undefined
Parallel lines
have the same slope
Perpendicular lines
opposite reciprocal
What is slope-intercept form?
y = 2x - 1
What is point-slope form?
y + 2 = 1/2x - 2
Angle Sum Theorem
The sum of all interior angles in a triangle = 180 degrees
Third Angle Theorem
If two sets of angles are congruent then the third angle in those triangles are congruent
Exterior Angle
angle formed by extension of one side of the triangle and an extension of another side
Remote Interior Angles
Interior angles that are not adjacent to given exterior angles
Exterior Angle Theorem
the sum of the two remote interior angles equals the exterior angle
Corollary 4.1
The 2 acute angles in a right triangle are complementary
Corollary 4.2
There can be at most one right angle or one obtuse angle in a triangle
Side-Side-Side Congruence (SSS)
If the sides of one triangle are congruent to the side of a second triangle, then the triangles are congruent
Side-Angle-Side Congruence (SAS)
If two sides and the included angle of one triangle are congruent to 2 sides and the included angle or another triangle, then the triangles are congruent
Angle-Side-Angle Congruence (ASA)
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent
Angle-Angle-Side Congruence (AAS)
If two angles and a non included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two angles are congruent
Vertex Angle
angle where the 2 congruent sides meet
Legs
the 2 congruent sides
Base
the side that is not congruent to the other sides
Base angles
angles formed by a base and a congruent side
Isosceles Triangle Theorem
If two sides of a triangle are congruent, then the angles opposite those sides are congruent
Converse of Isosceles Triangle Theorem
If two angles of a triangle are congruent, then the sides opposite those angles are congruent
Corollary 4.3
a triangle is equilateral if and only if it is equiangular
Corollary 4.4
Each angle of an equilateral triangle measures 60 degrees
Circumcenter Theorem
The circumcenter of a triangle is equidistant from the vertices of the triangle
Incenter Theorem
The Incenter of a triangle is equidistant from each side of the triangle
Centroid Theorem
The Centroid of a triangle is located two thirds of the distance from a vertex to the midpoint of the side opposite the vertex of a median
Exterior inequality Theorem
If an angle is an exterior angle of a triangle, then its measures is greater then the measure of either of its corresponding remote interior angles
Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side
SAS Inequality/Hinge Theorem
If two sides of a triangle are congruent to two sides of another triangle and the included angle in the other, the third side of the first triangle is longer than the third side of the second triangle
SSS Inequality Theorem
If two sides of a triangle are congruent to two sides of another triangle and the third side in one triangle is longer than the third side in the other, then the angle between the pair of congruent sides in the first triangle is greater than the corresponding angle in the second triangle
Perpendicular Bisectors
passes through the midpoint and is perpendicular to that side
Point of Concurrency
the point of intersection of three or more lines
Circumcenter
point of concurrency of the perpendicular bisectors of a triangle
Angle Bisectors
cuts an angle into two smaller congruent angles
Incenter
the point of concurrency of the angle bisectors
Median
a segment where the endpoints of a vertex and the midpoint of the opposite side
Centroid
the point of concurrency of the medians
Altitude
the segment from a vertex to the line containing the opposite side and is perpendicular to the line containing that side
Orthocenter
the point of concurrency of the altitudes
What do Circumcenters connect?
perpendicular bisectors
What do Incenters connect?
angle bisectors
What do Centroids connect?
medians
What do Orthocenters connect?
altitudes
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