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Theorem 1-1

Theorem 1-2

Theorem 1-3

Theorem 2-1 (Midpoint Theorem)

If two lines intersect, then they intersect in exactly one po…

Through a line and a point not in the line there is exactly o…

If two lines intersect, then exactly one plane contains the l…

If M is the midpoint of AB, then AM=v½ AB and MB= ½ AB

Theorem 1-1

If two lines intersect, then they intersect in exactly one po…

Theorem 1-2

Through a line and a point not in the line there is exactly o…

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate - part 1

1. The points on a line can be paired with the real numbers i…

If B is between A and C, then:... AB + BC = AC.

On line AB in a given plane, choose any point O between A and…

If point B lies in the interior if ∠AOC then ... m∠AOB + m∠BOC…

Ruler Postulate

1. The points on a line can be paired with the real numbers i…

Segment Addition Postulate

If B is between A and C, then:... AB + BC = AC.

Postulate 1 (Ruler Postulate)... p.12

Postulate 2 (Segment Addition Postulat…

Postulate 3 (Protractor Postulate)... p.18

Postulate 4 (Angle Addition Postulate)…

1. The points on a line can be paired with the real numbers i…

If B is between A and C, then AB+BC=AC

On AB in a given plane, choose an point O between A and B. Co…

If point B lies in the interior of ∠AOC, then m∠AOB + m∠BOC =…

Postulate 1 (Ruler Postulate)... p.12

1. The points on a line can be paired with the real numbers i…

Postulate 2 (Segment Addition Postulat…

If B is between A and C, then AB+BC=AC

Theorem 1-1

Theorem 1-2

Theorem 1-3

Theorem 2-1 (Midpoint Theorem)

If two lines intersect, then they intersect in exactly one po…

Through a line and a point not in the line there is exactly o…

If two lines intersect, then exactly one plane contains the l…

If M is the midpoint of AB, then AM=v½ AB and MB= ½ AB

Theorem 1-1

If two lines intersect, then they intersect in exactly one po…

Theorem 1-2

Through a line and a point not in the line there is exactly o…

Theorem 3-1

Theorem 3-2

Theorem 3-3

Theorem 3-4

If two parallel planes are cut by a third plane, then the lin…

If two parallel lines are cut by transversal, then alternate…

If two parallel lines are cut by transversal, Then same-side…

If a transversal is perpendicular to one of two parallel line…

Theorem 3-1

If two parallel planes are cut by a third plane, then the lin…

Theorem 3-2

If two parallel lines are cut by transversal, then alternate…

Theorem 1-1

Theorem 1-2

Theorem 1-3

Theorem 2-1 (Midpoint Theorem)

If two lines intersect, then they intersect in exactly one po…

Through a line and a point not in the line there is exactly o…

If two lines intersect, then exactly one plane contains the l…

If M is the midpoint of AB, then AM=v½ AB and MB= ½ AB

Theorem 1-1

If two lines intersect, then they intersect in exactly one po…

Theorem 1-2

Through a line and a point not in the line there is exactly o…

Ruler postulate

Segment addition postulate

Protractor postulate

Angle addition postulate

The points on a line can be paired with the real numbers in s…

If B is between A and C, ... then AB + BC = AC

On line AB in a given plane, choose any point O between A and…

If point B lies in the interior of <AOC, then m<AOB + m<BOC =…

Ruler postulate

The points on a line can be paired with the real numbers in s…

Segment addition postulate

If B is between A and C, ... then AB + BC = AC

alternate exterior angles

alternate interior angles

corresponding angles

parallel lines

Angles that lie outside a pair of lines and on opposite sides…

nonadjacent interior angles that lie on opposite sides of the…

Angles that lie on the same side of the transversal and in co…

lines in a plane that do not intersect

alternate exterior angles

Angles that lie outside a pair of lines and on opposite sides…

alternate interior angles

nonadjacent interior angles that lie on opposite sides of the…

Trapezoid

Exterior Angles

Interior Angles

Alternate Interior Angles

A quadrilateral with a pair of opposite sides parallel is cal…

The angles 1 and 8 are _________________________

The angles 2 and 6 are

The angles 2 and 5 are

Trapezoid

A quadrilateral with a pair of opposite sides parallel is cal…

Exterior Angles

The angles 1 and 8 are _________________________

Point

Ray

Line

Plane

Used to describe a location. Name with a capital letter.

A part of a line, with one endpoint, that continues without e…

A straight path that goes without end in two directions.

A flat surface that extends forever. Name a point with 3 nonc…

Point

Used to describe a location. Name with a capital letter.

Ray

A part of a line, with one endpoint, that continues without e…

Parallel Lines

Perpendicular Lines

Transversal line

Alternative Interior angles

Two lines that never touch

Two lines that intersect to make 90 degree angles

A line that passes through two lines in the same plane

Parallel Lines

Two lines that never touch

Perpendicular Lines

Two lines that intersect to make 90 degree angles

Parallel Lines

Skew Lines

Corresponding Angles

Alternate Interior Angles

Lines that do not intersect and that lie in the same plane.

Lines that do not intersect and that do not line in the same…

Parallel Lines

Lines that do not intersect and that lie in the same plane.

Skew Lines

Lines that do not intersect and that do not line in the same…

Parallel Lines

Perpendicular lines

Skew lines

Parallel Planes

Coplanar lines that do not intersect.... Their equations have th…

Lines that intersect at 90 degree angles.... Their slopes have a…

Lines that are not coplanar, not parallel and do not intersect.

Planes that do not intersect

Parallel Lines

Coplanar lines that do not intersect.... Their equations have th…

Perpendicular lines

Lines that intersect at 90 degree angles.... Their slopes have a…

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Same Side Interior Angles

Nonadjacent interior that lie on opposite sides of a transver…

Nonadjacent exterior angles that lie on opposite sides of the…

Angles that lie on the same side of the traversal and in corr…

Interior angles that lie on the same side of the transversal.…

Alternate Interior Angles

Nonadjacent interior that lie on opposite sides of a transver…

Alternate Exterior Angles

Nonadjacent exterior angles that lie on opposite sides of the…

angle

acute angle

obtuse angle

right angle

A figure formed by two rays with a common endpoint endpoint c…

An angle that is less than 90 degrees

An angle between 90 and 180 degrees

90 degree angle

angle

A figure formed by two rays with a common endpoint endpoint c…

acute angle

An angle that is less than 90 degrees

angle

interior of an angle

exterior of an angle

acute angle

a figure formed by two rays with a common endpoint called the…

the set of all points between the sides of the angle

the set of all points outside the angle

an angle that measures greater than 0 degrees and less than 9…

angle

a figure formed by two rays with a common endpoint called the…

interior of an angle

the set of all points between the sides of the angle

Counterexample

Good Definition has

Parallel Lines

Perpendicular Lines

something that would fit your definition, but is not what you…

classification, differentiation, and can be tested.

exist in the same plane that never meet. We use II to represe…

must meet at a 90° angle. We use ⊥ to represent it.

Counterexample

something that would fit your definition, but is not what you…

Good Definition has

classification, differentiation, and can be tested.

congruent figures

similar figures

line symmetry

transformation

closed plane figures that have the same size and shape

closed plane figures that have the same shape, but not necess…

A figure has line symmetry if a line can be drawn through the…

a transformation in a figure is a change in its position, sha…

congruent figures

closed plane figures that have the same size and shape

similar figures

closed plane figures that have the same shape, but not necess…

Quadrilateral

Trapezoid

Parallelogram

Rectangle

a flat shape with four straight sides. I am the most open clu…

a four sided figure with one pair of parallel sides.

a 4-sided flat shape with straight sides where opposite sides…

a 4-sided flat shape with straight sides where all interior a…

Quadrilateral

a flat shape with four straight sides. I am the most open clu…

Trapezoid

a four sided figure with one pair of parallel sides.

angle-angle similarity

angle

congruent

corresponding sides

if two angles of one triangle are congruent to two correspond…

in geometric figures, usually formed by two segments with a c…

exactly the same shape and size

sides in two or more figures that are images of each other wi…

angle-angle similarity

if two angles of one triangle are congruent to two correspond…

angle

in geometric figures, usually formed by two segments with a c…

isometry

congruent

CPCTC (CPCF)

Reflexive Property

composition of reflections, rotations, and translations

same size and shape

Corresponding Parts of Congruent Figures are Congruent

A is congruent to A

isometry

composition of reflections, rotations, and translations

congruent

same size and shape

point

line

plane

collinear

a location with no size and shape

made up of points and has no width or thickness; extends infi…

flat surface made up of points; has no depth and extends infi…

points on the same line

point

a location with no size and shape

line

made up of points and has no width or thickness; extends infi…

Coordinate

Distance

Betweenness of Points

Acute Angle

a number that corresponds to a position on an axis

Length between two points

Point B is between points A and C if and only if A,B, and C a…

an angle that measures less than 90 degrees

Coordinate

a number that corresponds to a position on an axis

Distance

Length between two points

postulate (axiom)

inductive reasoning

deductive reasoning

conjecture

an accepted statement of fact.

a type of reasoning that reaches conclusions based on a patte…

a process of reasoning logically from given facts to a conclu…

a conclusion reached by inductive reasoning (guess).

postulate (axiom)

an accepted statement of fact.

inductive reasoning

a type of reasoning that reaches conclusions based on a patte…

Parallel Lines

Skew lines

Transversal

Parallel Postulate

When two or more lines lie in the same plane and never inters…

Lines that are in different planes and never intersect.

A line that intersects two or more lines in different points

If there is a line and a point not on a line, then there is e…

Parallel Lines

When two or more lines lie in the same plane and never inters…

Skew lines

Lines that are in different planes and never intersect.

Parallel Lines

Skew Lines

Parallel planes

Transversal

Coplanar lines that do not intersect

Lines that do not intersect and are not coplanar

Planes that do not intersect

A line that intersects two or more lines.

Parallel Lines

Coplanar lines that do not intersect

Skew Lines

Lines that do not intersect and are not coplanar

Parallel Lines

Skew Lines

Parallel Planes

Parallel Line Postulate

Two lines that are coplanar and do not intersect

Lines that do not intersect and are not coplanar

Two planes that do not intersect

If there is a line and a point not on the line, then there is…

Parallel Lines

Two lines that are coplanar and do not intersect

Skew Lines

Lines that do not intersect and are not coplanar

Parallel Lines

Skew Lines

Transversal

Interior Angles

Two lines in the same plane that do not intersect

Two lines in different planes that do not intersect

A line that intersects two or more coplanar lines

Angles that lie in the region between the two lines

Parallel Lines

Two lines in the same plane that do not intersect

Skew Lines

Two lines in different planes that do not intersect

similarity

dilation

point of dilation / stretch point

scale factor / zoom factor

-same shape, but not necessarily the same size... -angles are co…

-a transformation where a point on a figure is stretched prop…

-the point of a figure that is stretched to form a dilation o…

-the number a side is multiplied by to make a bigger or small…

similarity

-same shape, but not necessarily the same size... -angles are co…

dilation

-a transformation where a point on a figure is stretched prop…

Construct

Classifying Triangles

Acute Triangle

Right Triangle

A tangent from a point outside a given circle to the circle

All equilateral triangles are isosceles

Three angles, each less than 90 degrees

One angle equals 90 segrees

Construct

A tangent from a point outside a given circle to the circle

Classifying Triangles

All equilateral triangles are isosceles

skew lines

parallel lines

parallel planes

transversal

lines that do not intersect and are no coplanar

lines that do not intersect and are coplanar

two planes that do no intersect

a line that intersects two or more coplanar lines at differen…

skew lines

lines that do not intersect and are no coplanar

parallel lines

lines that do not intersect and are coplanar

angle

vertex

right angle

parallel lines

A figure formed by two rays with a common endpoint

A point where two or more straight lines meet.

an angle that measures 90 degrees

lines that never intersect

angle

A figure formed by two rays with a common endpoint

vertex

A point where two or more straight lines meet.

Segment bisector

Perpendicular bisector

Perpendicular Bisector Conjecture

Converse of the Perpendicular Bisector…

A line, ray, or segment that passes through the midpoint of a…

A line or segment that divides a line segment into two equal…

If a point is on the perpendicular bisector of a segment, the…

If a point is equidistant from the endpoints of a segment, th…

Segment bisector

A line, ray, or segment that passes through the midpoint of a…

Perpendicular bisector

A line or segment that divides a line segment into two equal…

parallel lines

skew lines

parallel planes

transversal

lines in the same plane that never intersect

do not intersect and do not lie on the same plane

planes that do not intersect

a line that intersects two or more lines

parallel lines

lines in the same plane that never intersect

skew lines

do not intersect and do not lie on the same plane

acute

right

obtuse

straight

_______ angles measure between 0-90 degrees

______ angles measure exactly 90 degrees

______ angles measure between 90 and 180 degrees

______ angles measures exactly 180 degrees

acute

_______ angles measure between 0-90 degrees

right

______ angles measure exactly 90 degrees

Deductive Reasoning

Inductive Reasoning

2/3

1

The process of showing that certain statements follow... logical…

The process of observing data, recognizing patterns,... and maki…

Deductive Reasoning

The process of showing that certain statements follow... logical…

Inductive Reasoning

The process of observing data, recognizing patterns,... and maki…

Transversal

Interior

Exterior

Alternate Interior Angles

A line, ray, or segment that intersects two or more coplanar…

Area between the lines

Area outside the lines

Angles 2 and 7... Or... Angles 3 and 6

Transversal

A line, ray, or segment that intersects two or more coplanar…

Interior

Area between the lines

counterexample

right angle

acute angle

obtuse angle

an example that shows that a conjecture is incorrect or that…

an angle that measures 90 degrees

an angle that measures less than 90 degrees

an angle that measures more than 90 degrees but less than 180…

counterexample

an example that shows that a conjecture is incorrect or that…

right angle

an angle that measures 90 degrees

perpendicular lines

concurrent lines

point of concurrency

circumcenter

Lines that meet at right angles

3 or more lines that meat in a common point

the point where concurrent lines meet

the point of concurrency of 3 perpendicular bisectors

perpendicular lines

Lines that meet at right angles

concurrent lines

3 or more lines that meat in a common point