Good Morning – Geometry Tuesday, September 20 th

Good Morning – Geometry Good Morning – Geometry Tuesday, September 20Tuesday, September 20thth

HomeworkHomeworkCorrections on Summer Assignment TestCorrections on Summer Assignment Test– On separate paper, redo any problem where points On separate paper, redo any problem where points

were lostwere lost

Read Lesson 1.1, write vocabulary in your Read Lesson 1.1, write vocabulary in your Pictionary DictionaryPictionary Dictionary

Today’s AgendaToday’s AgendaSUMMER ASSIGNMENT TESTSUMMER ASSIGNMENT TESTVocabularyVocabulary

Geometry VocabularyGeometry VocabularyChapter 1Chapter 1

What is Geometry?What is Geometry?

Geometry is the study of Geometry is the study of shapesshapesThey studied Geometry They studied Geometry in Ancient Mesopotamia in Ancient Mesopotamia & Ancient Egypt& Ancient EgyptGeometry is important Geometry is important in the creation of art and in the creation of art and architecture.architecture.

Three basic building blocks of Three basic building blocks of GeometryGeometry

The three basics building blocks of The three basics building blocks of geometry are undefinable, however, they geometry are undefinable, however, they can be described and representedcan be described and represented– Point, line, planePoint, line, plane

●

POINTPOINTA POINT is the most basic building block of A POINT is the most basic building block of Geometry.Geometry.It has no size, only location. It has no size, only location. It is represented with a dot and named with a It is represented with a dot and named with a capital letter. capital letter. The Hershey Kiss represents a POINT on The Hershey Kiss represents a POINT on the line as does the red dotthe line as does the red dot

A●

H

LINELINE

D●

E●

PLANEPLANEA PLANE has length and width, but no A PLANE has length and width, but no thickness .thickness .(no, not the one that flies!) (no, not the one that flies!)

It is a flat surface that extends infinitely along its It is a flat surface that extends infinitely along its length and width. length and width. A plane is represented with a four-sided figure, A plane is represented with a four-sided figure, usually a parallelogram.usually a parallelogram.

A plane is named with a script capital letter, A plane is named with a script capital letter,

such as such as P P

PlanePlane

Imagine sitting on a row boat in the middle Imagine sitting on a row boat in the middle of the ocean. No matter which way you of the ocean. No matter which way you look…all you see is water…foreverlook…all you see is water…forever

DefinitionDefinition

A statement that clarifies or explains the A statement that clarifies or explains the meaning of a word or a phrasemeaning of a word or a phrase

– Square is a quadrilateral that is equiangular Square is a quadrilateral that is equiangular and equilateral.and equilateral.

CollinearCollinear

Points on the same linePoints on the same line– co = togetherco = together– linear = pertaining to a linelinear = pertaining to a line

On the line togetherOn the line together

Points A, B, & C are collinearPoints A, B, & C are collinear

●●

●

A

B

C

CoplanarCoplanarOn the same planeOn the same plane– co = togetherco = together– planar = pertaining to a planeplanar = pertaining to a plane

On the plane togetherOn the plane together

Points H & J and Line PQ are coplanar on Points H & J and Line PQ are coplanar on MM

●

●

●

●

H

J

P

Q

M

ENDPOINTENDPOINT

An ENDPOINT is a An ENDPOINT is a pointpoint at the end of a at the end of a ray or line segment. ray or line segment. (a capital letter)(a capital letter)

Endpoints

●

● ●

F

S B

LINE SEGMENTLINE SEGMENT

A LINE SEGMENT is A LINE SEGMENT is partpart of a ray or line. of a ray or line.It has It has twotwo endpoints endpoints

Name a line segment by its endpointsName a line segment by its endpoints

●●

Line Segment

Line Line

Endpoints

PQ

P Q

CONGRUENT CONGRUENT CONGRUENT means the CONGRUENT means the same size and same shapesame size and same shapeCONGRUENT LINE SEGMENTS means two line CONGRUENT LINE SEGMENTS means two line segments are the same sizesegments are the same size– Show congruent segments by making identical markings on Show congruent segments by making identical markings on

each.each.

– Parts with the Parts with the same amount same amount of markings are congruentof markings are congruent

● ●

● ●

Slash or tick marksIQER

THMA

E R

I Q

ATMH

AM

TH

MidpointMidpointMidpoint of a segment is the Midpoint of a segment is the pointpoint on the on the segment that is the same distance from both segment that is the same distance from both endpointsendpoints– bisects the segmentbisects the segment– divides the segment into two congruent segmentsdivides the segment into two congruent segments

Congruent markings on a segment indicate a Congruent markings on a segment indicate a point is a point is a midpointmidpoint

●●●

Congruent markings, aka, slash marks

QU E

Midpoint of WHAT?Midpoint of WHAT?

Can a point have a midpoint?Can a point have a midpoint?– a line?a line?– a square?a square?– a plane?a plane?

– NO, only a segment is finite in lengthNO, only a segment is finite in length– There is NO midpoint to infinityThere is NO midpoint to infinity

RAYRAYA RAY is part of a line, but it has A RAY is part of a line, but it has oneone endpoint and the other end continues endpoint and the other end continues infinitely.infinitely.

Name a ray with its Name a ray with its endpoint firstendpoint first, followed , followed by another point on the ray.by another point on the ray.

●

Endpoint

Raaaaaaaaaaaaaaaaaaaaaaaayyyyyyyyyyyyyyyyyyyyyyyyyyy

JK

J K●

Lesson 1.2-1.3Lesson 1.2-1.3

Angles and Angle Angles and Angle RelationshipsRelationships

ANGLESANGLESWhen you When you namename an angle. The an angle. The vertex/angle point goes in the middle of vertex/angle point goes in the middle of the name.the name.

A

B

C

If I wanted to know the measurement of Angle A…I would ask:” What is the measurement for

<BAC?” (Notice A is in the center)

Naming AnglesNaming AnglesA

A

TM

P

N M

CB

H

●

●

●

●

●

● ●●

● ●

<ABC, <CBA, <B

VERTEXVERTEXA VERTEX is a fancy name for “angle”A VERTEX is a fancy name for “angle”Two rays or lines that have the same Two rays or lines that have the same endpoint make a VERTEX/angleendpoint make a VERTEX/angleVERTEX/angles are measured in VERTEX/angles are measured in “degrees”“degrees”

The Corners of a square are its vertex/angles

When two lines cross, they make vertex/angles

VERTICAL LINEVERTICAL LINE

A VERTICAL LINE goes up & downA VERTICAL LINE goes up & down

The candy bars are vertical

HORIZONTAL LINEHORIZONTAL LINE

A HORIZONTAL LINE goes “across” (left A HORIZONTAL LINE goes “across” (left and right)and right)

The candy bars are Horizontal

PROTRACTORPROTRACTOR

We use a PROTRACTOR to measure We use a PROTRACTOR to measure vertex/angles in degreesvertex/angles in degrees

3 TYPES OF ANGLES3 TYPES OF ANGLES

ACUTE ANGLES are less than 90ACUTE ANGLES are less than 90°°

3 TYPES OF ANGLES3 TYPES OF ANGLES

RIGHT ANGLES measure exactly 90 RIGHT ANGLES measure exactly 90 °°

The “square” symbol means 90’

3 TYPES OF ANGLES3 TYPES OF ANGLES

OBTUES ANGLES are greater than 90 OBTUES ANGLES are greater than 90 ° ° but less than 180 °but less than 180 °

The EndThe End

Once you study all the fancy Once you study all the fancy words/vocabulary, Geometry is words/vocabulary, Geometry is very easy to understand…so very easy to understand…so

STUDY!STUDY!You are Learning a new Language.You are Learning a new Language.