Study sets matching "geometry geometric"

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Study sets matching "geometry geometric"

34 terms
Geometry geometric
Acute angle
Acute triangle
Adjacent angles
Base
Measures less than 90 degrees but more than 0 degrees
A triangle where all three internal angles are acute (less th…
Same common side same vertex
The number that is the stating point
Acute angle
Measures less than 90 degrees but more than 0 degrees
Acute triangle
A triangle where all three internal angles are acute (less th…
13 terms
Geometric Properties (Thinkwell Geometry)
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If a = b, then a+c = b+c
if a = b, then a-c = b-c
if a = b, the ac = bc
If a = b and c ≠ 0, the a/c = b/c
Addition Property of Equality
If a = b, then a+c = b+c
Subtraction Property of Equality
if a = b, then a-c = b-c
13 terms
Geometric Properties (Thinkwell Geometry)
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If a = b, then a+c = b+c
if a = b, then a-c = b-c
if a = b, the ac = bc
If a = b and c ≠ 0, the a/c = b/c
Addition Property of Equality
If a = b, then a+c = b+c
Subtraction Property of Equality
if a = b, then a-c = b-c
15 terms
Geometry algebraic and geometric proofs
addition property
subtraction property
multiplication property
division property
1.) If a=b, then a+c=b+c... 2.) If a=b, and c=d, then a+c=b+d... 3.…
1.) If a=b, then a-c=b-c... 2.) If a=b and c=d, then a-c=b-d... 3.)…
1.) If a=b, then ac=bc... 2.) Example: if 1/2xy=6 then xy=12
1.) If a=b, then a/c=b/c where x doesn't equal 0... 2.) Example:…
addition property
1.) If a=b, then a+c=b+c... 2.) If a=b, and c=d, then a+c=b+d... 3.…
subtraction property
1.) If a=b, then a-c=b-c... 2.) If a=b and c=d, then a-c=b-d... 3.)…
Geometrical Geometry
Triangle Sum Thm
Exterior Angle Thm
Base Angles Thm
Base Angles Thm Converse
The sum of the measures of the interior angles of a triangle…
The measure of an exterior angle of a triangle is equal to th…
If two angles are congruent, then the sides opposite them are…
If two angles are congruent, then the sides opposite them are…
Triangle Sum Thm
The sum of the measures of the interior angles of a triangle…
Exterior Angle Thm
The measure of an exterior angle of a triangle is equal to th…
Geometry Geometric mean
Geometric mean of triangle when split…
if x is the geo mean between a and b
Similar polygon's angles are
Polygon's sides are
Leg1/big hyp. =Pc1/leg1... Leg2/Big hyp.=Pc2/leg2... alt/Pc1 =Pc2…
X/a = b/X
congruent
proportional
Geometric mean of triangle when split…
Leg1/big hyp. =Pc1/leg1... Leg2/Big hyp.=Pc2/leg2... alt/Pc1 =Pc2…
if x is the geo mean between a and b
X/a = b/X
Geometric Shapes and Geometry Terms
Polygon
Quadrilateral
Angle
Right Angle
A flat shape with many sides.
A four-sided polygon.
The point where two lines meet.
90 degrees angle.
Polygon
A flat shape with many sides.
Quadrilateral
A four-sided polygon.
Geometry- Geometric Properties For Proofs
Reflective Property
Transitive Property
Symmetric Property
Addition Property of Equality
AB = AB... A quantity is equal to itself
If AB = BC and BC = EF, then AB = EF... If two qualities are eq…
If OA = AB, then AB = OA... If a quantity is equal to a second…
If AB = DF and BC = CD, then AB + BC = DF + CD... If equal quan…
Reflective Property
AB = AB... A quantity is equal to itself
Transitive Property
If AB = BC and BC = EF, then AB = EF... If two qualities are eq…
8 terms
Geometry - Unit 5 - Geometric and Algebraic Connections
Center of a Circle
Circle
Diameter
Pythagorean Theorem
The point inside the circle that is the same distance from al…
The set of all points in a plane that are the same distance,…
The distance across a circle through its center. The line seg…
A theorem that states that in a right triangle, the square of…
Center of a Circle
The point inside the circle that is the same distance from al…
Circle
The set of all points in a plane that are the same distance,…
30 terms
Geometry: Reasons and Geometric Proofs
Definition: IF 2 segments have the sam…
Postulate: IF B is between A & C THEN…
Definition: IF a point is a mid-point…
Definition: IF "something" bisects a s…
Definition of Congruent Segments
Segment Addition Postulate
Definition of a Midpoint
Definition of Segment Bisector
Definition: IF 2 segments have the sam…
Definition of Congruent Segments
Postulate: IF B is between A & C THEN…
Segment Addition Postulate
Geometry Chapter 2 - Geometric Reasoning
conjecture
counterexample
conditional statement
hypothesis
an educated guess
shows why the conjecture is incorrect
if/then statement
'if' part
conjecture
an educated guess
counterexample
shows why the conjecture is incorrect
11 terms
Geometry Chapter 2 - Geometric Reasoning
Counterexample
Conjecture
Inductive Reasoning
Deductive Reasoning
An example that proves a conjecture is false. It could be a d…
A statement that is believed to be true.
The process of reaching a conclusion from a pattern, specific…
The process of reaching a conclusion by using logic based on…
Counterexample
An example that proves a conjecture is false. It could be a d…
Conjecture
A statement that is believed to be true.
9 terms
Geometry Chapter 8: Geometric Inequalities
Addition Property
Subtraction Property
Multiplication Property
Transitive Property
if a < b, then a + c < b + c;... if a < b and c < d, then a + c…
if a < b, then a - c < b - c
if a < b and c > 0, then ac < bc
if a < b and b < c, then a < c
Addition Property
if a < b, then a + c < b + c;... if a < b and c < d, then a + c…
Subtraction Property
if a < b, then a - c < b - c
18 terms
Geometry Chapter 2 - Geometric Reasoning
contrapositive
conjunction
converse
truth table
a statement that negates both the hypothesis and conclusion o…
two statements joined by "and"
a statement that exchanges the hypothesis and conclusion of t…
a method for organizing the truth values of statements
contrapositive
a statement that negates both the hypothesis and conclusion o…
conjunction
two statements joined by "and"
9 terms
Geometric Properties (Thinkwell Geometry)
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If a = b, then a+c = b+c
if a = b, then a-c = b-c
if a = b, the ac = bc
If a = b and c ≠ 0, the a/c = b/c
Addition Property of Equality
If a = b, then a+c = b+c
Subtraction Property of Equality
if a = b, then a-c = b-c
9 terms
Geometry Vocabulary for Geometric Proofs
Segment Addition Postulate
Angle Addition Postulate
Reflexive Property
XY≅VW, so VW≅XY
If B is between A and C then AB+BC=AC
If D is on the interior Angle ABC then Angle ABD+DBC=ABC
AB ≅ AB or equal too( line on top of letters)
Symmetric
Segment Addition Postulate
If B is between A and C then AB+BC=AC
Angle Addition Postulate
If D is on the interior Angle ABC then Angle ABD+DBC=ABC
Geometry and Geometric shapes
Geometry
Protracter
Compass
Straightedge
The branch of mathematics that treats the properties
Used for measuring angles
Containing a magnetized pointer
Accurate straightedge
Geometry
The branch of mathematics that treats the properties
Protracter
Used for measuring angles
13 terms
Geometry Vocab - Geometric Figures
Point
Line
Line Segment
Ray
Named with a capital letter
Named using any two points on the line, or named using a lowe…
Named using the two end points
Named using the endpoint first then one other point, endpoint…
Point
Named with a capital letter
Line
Named using any two points on the line, or named using a lowe…
Geometric Properties: Geometry
Vertical Angles Theorem
Transitive Prop of Congruence
Congruent Complements Theorem
Congruent Supplement Theorem
Vertical angles are congruent
If two angles (segments/shapes/etc) are congruent to the same…
If two angles are complementary to the same angle then they a…
If two angles are supplementary to the same angle then they a…
Vertical Angles Theorem
Vertical angles are congruent
Transitive Prop of Congruence
If two angles (segments/shapes/etc) are congruent to the same…
Geometry: Trigonometry Geometric Mean
tan 81
sin 2
tan 63
tan 9
6.31
0.035
1.96
0.16
tan 81
6.31
sin 2
0.035
Geometric Figures (Geometry 2a)
Point
Line
Plane
cone
a dot or other punctuation mark, in particular a period.
a long, narrow mark or band.
a flat surface on which a straight line joining any two point…
a solid or hollow object that tapers from a circular or rough…
Point
a dot or other punctuation mark, in particular a period.
Line
a long, narrow mark or band.
Geometric Properties (Thinkwell Geometry)
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If a = b, then a+c = b+c
if a = b, then a-c = b-c
if a = b, the ac = bc
If a = b and c ≠ 0, the a/c = b/c
Addition Property of Equality
If a = b, then a+c = b+c
Subtraction Property of Equality
if a = b, then a-c = b-c
13 terms
Geometric & Electron Geometry
AX₂
AX₃
AX₂E
AX₄
MG & EG - Linear... Bond Angle: 180°
MG & EG - Trigonal Planar ... Bond Angle: 120°
MG: Bent ... EG: Trigonal Planar... Bond Angle: <120°
MG + EG : Tetrahedral... Bond angle: 109.5°
AX₂
MG & EG - Linear... Bond Angle: 180°
AX₃
MG & EG - Trigonal Planar ... Bond Angle: 120°
Discovering Geometry: Geometric Art
symmetry
bilateral symmetry
reflectional symmetry
line of symmetry
...
...
...
...
symmetry
...
bilateral symmetry
...
Geometry Geometric Reasoning Vocab
Inductive Reasoning
Deductive Reasoning
Conjecture
Counterexample
Process of ruling a statement true because specific cases are…
Using logic and facts to draw conclusions
A statement made as a result of inductive or deductive reason…
Example that proves a conjecture false
Inductive Reasoning
Process of ruling a statement true because specific cases are…
Deductive Reasoning
Using logic and facts to draw conclusions
Geometric Properties (Thinkwell Geometry)
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
If a = b, then a+c = b+c
if a = b, then a-c = b-c
if a = b, the ac = bc
If a = b and c ≠ 0, the a/c = b/c
Addition Property of Equality
If a = b, then a+c = b+c
Subtraction Property of Equality
if a = b, then a-c = b-c
Geometry, Chapter 2.6, Geometric Proof
theorem
two-column proof
Linear Pair Theorem
Congruent Supplements Theorem
any statement that you can prove
list the steps of the proof in the left column, and the match…
if two angles form a linear pair, then they are supplementary
If two angles are supplementary to the same angle (or to two…
theorem
any statement that you can prove
two-column proof
list the steps of the proof in the left column, and the match…
Geometry (introduction to geometric proof)
addition property of equality
subtraction property of equality
multiplication property of equality
division property of equality
if a = b, then a + c = b + c
if a = b, then a - c = b - c
if a = b, then a c = b c
if a = b and c does not equal 0, then a/c = b/c
addition property of equality
if a = b, then a + c = b + c
subtraction property of equality
if a = b, then a - c = b - c
Geometry Triangles and Geometric mean
45-45-90 Triangles
30-60-90 Triangles
Geometric mean
Proportion 1
x, x, and x√2
x, 2x, x√3
Proportions solving for x
Tent 1/Grass 1 = Grass 1 +2/Tent 1
45-45-90 Triangles
x, x, and x√2
30-60-90 Triangles
x, 2x, x√3
15 terms
Electron Geometric & Molecular Geometry
No. of Attachments: 2... Lone Pairs: 0
No. of Attachments: 3... Lone Pairs: 0
No. of Attachments: 2... Lone Pairs: 1
No. of Attachments: 4... Lone Pairs: 0
Family: Linear... Shape: Linear... Hybrid: sp (triple bond)
Family: Trigonal Planar... Shape: Trigonal Planar... Hybrid: sp2
Family: Trigonal Planar... Shape: Bent... Hybrid: sp2
Family: Tetrahedral... Shape: Tetrahedral... Hybrid: sp3
No. of Attachments: 2... Lone Pairs: 0
Family: Linear... Shape: Linear... Hybrid: sp (triple bond)
No. of Attachments: 3... Lone Pairs: 0
Family: Trigonal Planar... Shape: Trigonal Planar... Hybrid: sp2
20 terms
Geometry-Geometric proofs
Segment Addition Postulate
Angle Addition Postulate
Congruent Angles
Complementary Angles
line AB + line BC=line AC
m<ABC + m<CBD = m<ABD
Angles with the same measure
2 angles with the sum of 90 degrees
Segment Addition Postulate
line AB + line BC=line AC
Angle Addition Postulate
m<ABC + m<CBD = m<ABD
8 terms
GSE Geometry - Unit 5: Geometric and Algebraic Connections
Center of a circle
Circle
Conic section
diameter
the point inside a circle that is the same distance from all…
Is the set of points which are all the same distance (its rad…
a figure formed by the intersection of a plane and a right ci…
The distance across a circle through its center. The line seg…
Center of a circle
the point inside a circle that is the same distance from all…
Circle
Is the set of points which are all the same distance (its rad…
GSE Geometry - Unit 5: Geometric and Algebraic Connections
Center of a circle
Circle
Conic section
diameter
the point inside a circle that is the same distance from all…
Is the set of points which are all the same distance (its rad…
a figure formed by the intersection of a plane and a right ci…
The distance across a circle through its center. The line seg…
Center of a circle
the point inside a circle that is the same distance from all…
Circle
Is the set of points which are all the same distance (its rad…
14 terms
GEOMETRY - Geometric Figures (14 Questions)
triangle
rectangular solid
cone
parallelogram
Has 3 sides and 3 angles.
Has 6 faces, all angles are 90 degrees, all pairs of opposite…
Has a circular base and tapers to the vertex.
Has 4 sides; opposite sides have equal lengths and are parall…
triangle
Has 3 sides and 3 angles.
rectangular solid
Has 6 faces, all angles are 90 degrees, all pairs of opposite…
Geometry Chapter 2 - Geometric Reasoning
Inductive Reasoning
Conjecture
Counterexample
Conditional Statement
The process of reasoning that a rule or statement is true bec…
A statement you believe to be true based on inductive reasoni…
One example that shows the conjecture is false.
If P, then Q. P -> Q ... P is the Hypothesis and Q is the conclu…
Inductive Reasoning
The process of reasoning that a rule or statement is true bec…
Conjecture
A statement you believe to be true based on inductive reasoni…
Geometry (Sabor): Benchmark 1 - Basic Geometrical Objects and Geometric Relationships
line
midpoint
plane
point
an infinite path where each connected piece is a segment
the point halfway between the endpoints of a segment; bisects…
a flat surface that continues forever and has no thickness (l…
a location that does not take up space; usually labeled with…
line
an infinite path where each connected piece is a segment
midpoint
the point halfway between the endpoints of a segment; bisects…
Unit 2 Geometry (Geometric Reasoning)
Conditional Statement
Converse
Inverse
Contrapostive
a statement that can be written in the form "If p, then q"
statement formed by exchanging the hypothesis and conclusion…
Statement formed by negating the hypothesis and conclusion "n…
statement formed by switching and negating the hypothesis and…
Conditional Statement
a statement that can be written in the form "If p, then q"
Converse
statement formed by exchanging the hypothesis and conclusion…
21 terms
Geometric Definition (Mr. Hiller Geometry)
collinear
line segment
midpoint of a segment
bisector of a segment
two or more points that are on the same line
a collinear set of points bounded by two endpoints
a point dividing a line segment into two equal lengths
a line dividing a line segment into two equal lengths
collinear
two or more points that are on the same line
line segment
a collinear set of points bounded by two endpoints
7 terms
Geometry Unit 1: Geometric Transformations
Translations
Reflections: x-axis
Reflections: y-axis
Reflections: x=y
(x,y) -> (x+?,y+?)
(x,y) -> (x,-y)
(x,y) -> (-x,y)
(x,y) -> (y,x)
Translations
(x,y) -> (x+?,y+?)
Reflections: x-axis
(x,y) -> (x,-y)
Geometry Chapter 2 - Geometric Reasoning
Counterexample
Conjecture
Inductive Reasoning
Deductive Reasoning
An example that proves a conjecture is false. It could be a d…
A statement that is believed to be true.
The process of reaching a conclusion from a pattern, specific…
The process of reaching a conclusion by using logic based on…
Counterexample
An example that proves a conjecture is false. It could be a d…
Conjecture
A statement that is believed to be true.
15 terms
VSEPR Geometric Family (Electronic Geometry)
Linear
Trigonal planar
Trigonal planar
Tetrahedral
Linear
Trigonal planar
25 terms
Geometry Chapter 2: Geometric reasoning
Inductive Reasoning
conjecture
counterexample
conditional statement
the process of reasoning that a rule or statement is true bec…
a statement you believe to be true based on inductive reasoning
an example that shows a conjecture is false
if p then q
Inductive Reasoning
the process of reasoning that a rule or statement is true bec…
conjecture
a statement you believe to be true based on inductive reasoning
45 terms
Geometry EOC Review (postulates and geometric meme)
Reflexive Property
Symmetric Property
Transitive Property
Addition Postulate
A quantity is congruent (equal) to itself. a = a
If a = b, then b = a.
If a = b and b = c, then a = c.
If equal quantities are added to equal quantities, the sums a…
Reflexive Property
A quantity is congruent (equal) to itself. a = a
Symmetric Property
If a = b, then b = a.
7 terms
Praxis II 0069 Geometry: Geometric Transformations
geometric transformation
preimage
translation
reflection
a mapping between two sets of points such that each points in…
each point in the preimage has a unique image
a slide in a horizontal or vertical direction
a flip across a line, new figure is a mirror image of the ori…
geometric transformation
a mapping between two sets of points such that each points in…
preimage
each point in the preimage has a unique image
12 terms
Prentice Hall Geometry Basic Geometric Formulas
Area Of A Rectangle
Base
Altitiude
Height
The Area of a rectangle is the product of its base and height…
any part of a parallelogram's sides(most likely the bottom).
A segment perpendicular to the line containing that base draw…
The length of the altitude
Area Of A Rectangle
The Area of a rectangle is the product of its base and height…
Base
any part of a parallelogram's sides(most likely the bottom).
7 terms
Praxis II 0069 Geometry: Geometric Transformations
geometric transformation
preimage
translation
reflection
a mapping between two sets of points such that each points in…
each point in the preimage has a unique image
a slide in a horizontal or vertical direction
a flip across a line, new figure is a mirror image of the ori…
geometric transformation
a mapping between two sets of points such that each points in…
preimage
each point in the preimage has a unique image
Geometry Chapter 2: Geometric Reasoning Vocabulary
2.1 angle
2.1 line
2.1 midpoint
2.1 plane
a figure formed by two rays with a common endpoint
a straight path formed by two rays with a common endpoint
a point that divides a segment into two congruent segments
a flat surface that has no thickness and extends forever
2.1 angle
a figure formed by two rays with a common endpoint
2.1 line
a straight path formed by two rays with a common endpoint
Honors geometry: geometric and algebraic connections
Y1-y2=m(x1-x2)
Y=mx+b
AB=<(x1-x2)^2+(y1-y2)^2
X1+1/2(x2-X1)
Point slope form
Slope intercept form
Distance formula
Midpoint of a segment
Y1-y2=m(x1-x2)
Point slope form
Y=mx+b
Slope intercept form
Geometry Chapter 2 Geometric Proofs
Ruler Postulate
Segment Addition Postulate
Protractor Postulate
Angle Addition Postulate
The point on a line can be put into a one to one corresponden…
If B is between A and C, then AB + BC = AC.
Given ↔AB and a point O on ↔AB, all rays that can be drawn fr…
If S is in the interior of ∠PQR, then m∠PQS + m∠SQR = m∠PQR.
Ruler Postulate
The point on a line can be put into a one to one corresponden…
Segment Addition Postulate
If B is between A and C, then AB + BC = AC.
21 terms
Geometry Chapter 2 - Geometric Reasoning
Inductive Reasoning
Conjecture
Counterexample
Conditional Statement
The process of reasoning that a rule or statement is true bec…
A statement you believe to be true based on inductive reasoni…
One example that shows the conjecture is false.
If P, then Q. P -> Q ... P is the Hypothesis and Q is the conclu…
Inductive Reasoning
The process of reasoning that a rule or statement is true bec…
Conjecture
A statement you believe to be true based on inductive reasoni…
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