#### Study sets matching "term:geometry = euclid"

#### Study sets matching "term:geometry = euclid"

point

line

straight line

surface

that which has no part

breathless length ... --the extremities of a line are points

a line which lies evenly with the points on itself

that which has length and breadth only ... --the extremities of…

point

that which has no part

line

breathless length ... --the extremities of a line are points

Axiom1

Axiom2

Axiom3

Axiom4

Things which are equal to the same thing are equal to one ano…

If Equals are added to equals,the wholes are equal

If equals are subtracted from equals,the remainders are equal

Things which coincide with one another are equal to one another

Axiom1

Things which are equal to the same thing are equal to one ano…

Axiom2

If Equals are added to equals,the wholes are equal

Point

Line

Straight line

Surface

That which has no part. The extremities of a line.

Breadthless length. The extremities of a surface.

A line which lies evenly with the points on itself.

That which has length and breadth only.

Point

That which has no part. The extremities of a line.

Line

Breadthless length. The extremities of a surface.

point

line

straight line

surface

that which has no part

breathless length ... --the extremities of a line are points

a line which lies evenly with the points on itself

that which has length and breadth only ... --the extremities of…

point

that which has no part

line

breathless length ... --the extremities of a line are points

#1: AB and CD are equally distant from…

Point D is center of the circle

Straight line joined from G to F and p…

A line joined from F to G passes throu…

#1: Circle ABCD, AB and CD are equal straight lines... #2: Circl…

Circle ABC with point D inside it, and DA, DB, and DC fall up…

Circles ABC, ADE touching internally at A, and F is the cente…

Circles ABC, ADE touching at A externally, F the center of AB…

#1: AB and CD are equally distant from…

#1: Circle ABCD, AB and CD are equal straight lines... #2: Circl…

Point D is center of the circle

Circle ABC with point D inside it, and DA, DB, and DC fall up…

Postulate1

Postulate2

Postulate3

Postulate4

A straight line may be drawn from any one point to any other…

A terminated line can be produced indefinitely

A circle can be drawn with any centre and any radius

All right angles are equal to one another

Postulate1

A straight line may be drawn from any one point to any other…

Postulate2

A terminated line can be produced indefinitely

Prop 4

Prop 5

Prop 6

Prop 8

SAS

If a triangle is isosceles then the base angles are congruent.

If two angles in a triangle are congruent then the two opposi…

If three corresponding sides of one triangle are congruent to…

Prop 4

SAS

Prop 5

If a triangle is isosceles then the base angles are congruent.

first postulate

second postulate

third postulate

fourth postulate

To draw a straight line from any point to any point.

To produce a finite straight line continuously in a straight…

To describe a circle with any center and distance.

That all right angles are equal to one another.

first postulate

To draw a straight line from any point to any point.

second postulate

To produce a finite straight line continuously in a straight…

Definition 1

Definition 2

Definition 4

Definition 10

A point is that which has no part.

A line is breadthless length.

A straight line is a line which lies evenly with the points o…

When a straight line set up on a straight line makes the adja…

Definition 1

A point is that which has no part.

Definition 2

A line is breadthless length.

I.1

I.2

I.3

I.4

Construct an equilateral triangle on a given line.

Construct a line equal to a given line at a given point.

Cut a line equal to a given line from a given longer line.

If two triangles have two sets of sides and the angle between…

I.1

Construct an equilateral triangle on a given line.

I.2

Construct a line equal to a given line at a given point.

Midpoint

Slope

Distance

Parallel lines

The middle point of a line segment

Thus describes the direction and steepness of a line.

This describes the length of a segment or how far apart an ob…

Two lines that never meet.

Midpoint

The middle point of a line segment

Slope

Thus describes the direction and steepness of a line.

Geometry

Euclidean Geometry

Undefined terms

Point

word composed of two Greek terms, "geos" meaning earth and "m…

identifies a geometry which Euclid formalized and which was a…

terms in Euclidean geometry which mathematicians consider onl…

one of the undefined terms; it has only position and has no l…

Geometry

word composed of two Greek terms, "geos" meaning earth and "m…

Euclidean Geometry

identifies a geometry which Euclid formalized and which was a…

Geometry

Euclidean Geometry

Undefined terms

Point

word composed of two Greek terms, "geos" meaning earth and "m…

identifies a geometry which Euclid formalized and which was a…

terms in Euclidean geometry which mathematicians consider onl…

one of the undefined terms; it has only position and has no l…

Geometry

word composed of two Greek terms, "geos" meaning earth and "m…

Euclidean Geometry

identifies a geometry which Euclid formalized and which was a…

Book 1

Book 2

Book 3

Book 4

-triangles, parallelograms, parallel lines... -1.47 Pythagorean…

-Divided lines and areas they give rise to... -straight lines di…

-Circles ... -diameter, tangent, angles in circles, segments of…

-Regular polygons and their relationship with circles... -inscri…

Book 1

-triangles, parallelograms, parallel lines... -1.47 Pythagorean…

Book 2

-Divided lines and areas they give rise to... -straight lines di…

point

line

line segment

ray

A location; it has no dimension. Represented by a dot.

A straight path that continues forever in both directions; ha…

Part of a line; has two endpoints.

Part of a line; has one endpoint and the other end goes on fo…

point

A location; it has no dimension. Represented by a dot.

line

A straight path that continues forever in both directions; ha…

Geometry

Euclidean Geometry

Undefined terms

Point

word composed of two Greek terms, "geos" meaning earth and "m…

identifies a geometry which Euclid formalized and which was a…

terms in Euclidean geometry which mathematicians consider onl…

one of the undefined terms; it has only position and has no l…

Geometry

word composed of two Greek terms, "geos" meaning earth and "m…

Euclidean Geometry

identifies a geometry which Euclid formalized and which was a…

D1. Point

D2. Line

D3. Extremities of lines

D4. Straight line

A point is that which has no part.

A line is a breadthless length.

The extremities of a line are points.

A straight line is a line which lies evenly with the points o…

D1. Point

A point is that which has no part.

D2. Line

A line is a breadthless length.

Geometry

Euclidean Geometry

Undefined terms

Point

word composed of two Greek terms, "geos" meaning earth and "m…

identifies a geometry which Euclid formalized and which was a…

terms in Euclidean geometry which mathematicians consider onl…

one of the undefined terms; it has only position and has no l…

Geometry

word composed of two Greek terms, "geos" meaning earth and "m…

Euclidean Geometry

identifies a geometry which Euclid formalized and which was a…

Geometry

Euclidean Geometry

Undefined terms

Point

word composed of two Greek terms, "geos" meaning earth and "m…

identifies a geometry which Euclid formalized and which was a…

terms in Euclidean geometry which mathematicians consider onl…

one of the undefined terms; it has only position and has no l…

Geometry

word composed of two Greek terms, "geos" meaning earth and "m…

Euclidean Geometry

identifies a geometry which Euclid formalized and which was a…

Geometry

Euclidean Geometry

Undefined terms

Point

word composed of two Greek terms, "geos" meaning earth and "m…

identifies a geometry which Euclid formalized and which was a…

terms in Euclidean geometry which mathematicians consider onl…

one of the undefined terms; it has only position and has no l…

Geometry

word composed of two Greek terms, "geos" meaning earth and "m…

Euclidean Geometry

identifies a geometry which Euclid formalized and which was a…

1. a point

2. a line

3. ends (extremities) of a line

4. a straight line

A point is that which has no parts.

A line is length without width.... [We normally today use the te…

The ends of a line are points.

A straight line is a line that lies symmetrically with the po…

1. a point

A point is that which has no parts.

2. a line

A line is length without width.... [We normally today use the te…

father of Geometry

segment addition postulate

Postulate 1:1

Point

Euclid

If A, B, C, are collinear and B is between A and C, then AB+…

through any 2 points there is exactly one line

A location in the coordinate plane. Symbol- A

father of Geometry

Euclid

segment addition postulate

If A, B, C, are collinear and B is between A and C, then AB+…

Postulate 1

Postulate 2

Postulate 3

Postulate 4

a straight line can be drawn from any point to any point

a finite straight line can be produced continuously in a stra…

a circle may be described with any center and distance

all right angles are equal to one another

Postulate 1

a straight line can be drawn from any point to any point

Postulate 2

a finite straight line can be produced continuously in a stra…

Undefined Terms

Angle

Acute Angle

Euclid

point, line, plane

the union of two rays with a common endpoint

An angle whose measure is less than 90º

The father of Geometry, wrote "The Elements"

Undefined Terms

point, line, plane

Angle

the union of two rays with a common endpoint

Composition of Transformations

Congruent segments

Degree of Rotation

Dilation

combination of two or more transformations

line segments whose lengths are equal

number of degrees a figure is rotated about the point (center…

a similarity transformation in which a figure is enlarged or…

Composition of Transformations

combination of two or more transformations

Congruent segments

line segments whose lengths are equal

Geometry

Euclidean Geometry

Undefined terms

Point

word composed of two Greek terms, "geos" meaning earth and "m…

identifies a geometry which Euclid formalized and which was a…

terms in Euclidean geometry which mathematicians consider onl…

one of the undefined terms; it has only position and has no l…

Geometry

word composed of two Greek terms, "geos" meaning earth and "m…

Euclidean Geometry

identifies a geometry which Euclid formalized and which was a…

Surface

Edges

Plane Surface or (Plane)

Plane angle

Something with two dimensions

If a surface has edges then the edges (or boundaries) are lin…

A surface which lies evenly with the straight lines on itself…

The inclination to one another of two lines in a plane which…

Surface

Something with two dimensions

Edges

If a surface has edges then the edges (or boundaries) are lin…

The Hellenistic Period 300 B.C.E-100 B…

Alexander the Great

The Museum... Many people went when the f…

Euclid

What was the most productive periods in history for math?

Who founded Alexandria, Egypt?

What was the famous school in Alexandria?

Who studied at the famous school in Alexandria?

The Hellenistic Period 300 B.C.E-100 B…

What was the most productive periods in history for math?

Alexander the Great

Who founded Alexandria, Egypt?

geometry

Euclid

three undefined terms of geometry

point

study of shapes, means the measure of the Earth.

lived 500 BCE, father of geometry, axiomatic method

point... line... plane

no size... represented by a dot,•A

geometry

study of shapes, means the measure of the Earth.

Euclid

lived 500 BCE, father of geometry, axiomatic method

line segment

collinear

noncollinear

concurrent

a part of a line bounded by 2 endpoints

points that are on the same line

points that are not on the same line

lines that contain the same point

line segment

a part of a line bounded by 2 endpoints

collinear

points that are on the same line

"The Knowledge of which geometry aims…

"There is no royal road to geometry"

"... being perpetually charmed by his…

"Which was to be proved."

Plato, The Republic

Euclid

Plutarch, The life of Archimedes

Euclid, The elements

"The Knowledge of which geometry aims…

Plato, The Republic

"There is no royal road to geometry"

Euclid

Ways to prove lines parallel (7 of them)

corresponding angles

Alternative Interior angles

Alternative Exterior Angles

converse corresponding angle post... converse alt interior angle…

1 & 5,... 3 & 7,... 2 & 6, ... 4 & 8

3 & 6... 4 & 5

1 & 8... 2 & 7

Ways to prove lines parallel (7 of them)

converse corresponding angle post... converse alt interior angle…

corresponding angles

1 & 5,... 3 & 7,... 2 & 6, ... 4 & 8

Who is the "father of geometry"

What did Euclid write?

Point

Line

Euclid of Alexandria

The Elements

Indication of an exact location. A point has location and not…

A straight, unbroken set of points that goes on forever. It h…

Who is the "father of geometry"

Euclid of Alexandria

What did Euclid write?

The Elements

Point

Line

Plane

Euclid

Names location, has no dimensions (0 dimensional)

Straight path that goes forever in both directions, has no wi…

Flat surface that extends forever, has no thickness (2 dimens…

Father of geometry

Point

Names location, has no dimensions (0 dimensional)

Line

Straight path that goes forever in both directions, has no wi…

Euclid

point

line

line segment

Greek mathematician who organized known geometry in the 4th c…

shown by a dot, it is a location in space

extends infinitely

part of a line with a beginning and ending point

Euclid

Greek mathematician who organized known geometry in the 4th c…

point

shown by a dot, it is a location in space

point

line

line segment

ray

A location; it has no dimension. Represented by a dot.

A straight path that continues forever in both directions; ha…

Part of a line; has two endpoints.

Part of a line; has one endpoint and the other end goes on fo…

point

A location; it has no dimension. Represented by a dot.

line

A straight path that continues forever in both directions; ha…

net

geometry

Euclid

Three Undefined Terms

a two-dimensional diagram that can be folded to form a three-…

- the measure of the earth... - the study of shapes

@ 500 B.C.E.... - father of geometry... - axiomatic era

- point... - line... - plane

net

a two-dimensional diagram that can be folded to form a three-…

geometry

- the measure of the earth... - the study of shapes

Eudoxus

Eudoxus theory of proportion

Eudoxus theory of Exhaustion

Alexander the Great

geometry and astronomy (has craters name after self)

a,b,c,,d where a/b=c/d... (m

**a>n**b) implies (m**c>n**d)... (m**a=n**b)…-areas of a circle are to one another as the squares of their…

-expanded Greece in 13 years ... -names at least 70 cities after…

Eudoxus

geometry and astronomy (has craters name after self)

Eudoxus theory of proportion

a,b,c,,d where a/b=c/d... (m

**a>n**b) implies (m**c>n**d)... (m**a=n**b)…