Opening Activity

Give an example of a point, line and plane that can be found in the classroom.

1.1 POINTS, LINES, & PLANES

Geometry Online Textbook

Foldable Activity

What is a definition?

Known words used to describe a new word

Undefined terms – not formally defined

There are 3 in geometry.

Point Line Plane

Point

1. Has no dimension (no length, width,

thickness)

2. Usually represented by a

dot

3. Named using one capital letter, B

LineExtends forever in one dimension (length)Has an arrowhead on each end representing the fact that it goes on foreverConsists of an infinite amount of points

Always straight

Named with a lowercase script letter or by 2 points on the line

A B

l

Can be called:

Line l

Line AB or AB

Line BA or BA

PlaneExtends forever in 2 dimensions (length &

width)

A flat surface consisting of

infinitely many points

Usually represented by a 4-sided figure

Named with a capital script letter or 3 points on the

surface of the plane

A

BC

W Can be named:

Plane W

Plane ABC, plane BCA, plane CBA, etc.

More Definitions

Collinear points – points that lie on the same line

Coplanar points – points that lie on the same plane

Space – a boundless, three-dimensional set of all points. Space can contain lines and planes.

IDENTIFY AND NAME THE FOLLOWING:

POINT LINE PLANE COLLINEAR POINTS NONCOLLINEAR POINTS COPLANAR POINTS NONCOPLANAR POINTS

Practice

Assignment

Handout

Warm up

Practice

1.2 LINEAR MEASURES

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Line Segment (or segment)

A section of a line that has 2 endpoints

Named by its endpoints. AB or BA

The length or measure of AB is written as AB.

A B

Example:

Find the length of AB using the ruler.

A B

BETWEENNESS OF POINTS

AB + BC = AC.

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

PRACTICE

Find the value of the variable and LM if L is between N and M.

1. NL = 5x, LM = 3x, and NL = 15

2. NL = 6x – 5, LM = 2x + 3, and NM = 30

CONGRUENT SEGMENTS

Two segments having the same measure are congruent.

is read is congruent to. (Red slashes indicate t he segments are congruent.)

2 cm 2 cm

Independent Practice

Handout Homework Page 17 22 – 39 all

1.3 DISTANCE AND

MIDPOINTS

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Warm up

Practice

DISTANCE BETWEEN TWO POINTS

NUMBER LINE COORDINATE PLANE

PQ = | b – a | or | a – b |

Example Find the distance

between the two points -5 and 1.

The distance between d between two points with coordinates

(x2 - x1) and (y2 – y1) is given by

d = √ (x2 – x1)2 + (y2 – y1)2

Example Find the distance

between R(5.1) and S(-3,-3).

Midpoint of a Segment

Used for finding the coordinates of the midpoint of a segment in a coordinate plane.

If the endpoints are (x1,y1) & (x2,y2), then

2,

22121 yyxx

Ex: Find the midpoint of SP if S(-3,-5) & P(5,11

Ex: The midpoint of AB is M(2,4). One endpoint is A(-1,7). Find the coordinates of B.

)midpoint(2

,2

2121

yyxx

Independent Practice

Handout Homework Page 25-26 13-18 all; 23-28 all; 31 - 44

all Quiz next block on Sections 1-1 to 1-3 You must know the Distance and Midpoint

Formulas Study!!!!

1.4 ANGLE MEASURES

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Warm up

Practice

Angle symbol: 2 rays that share the same endpoint (or

initial point)

Y

Z

X

Sides – the rays XY & XZ

Vertex – the common endpoint; X

Named <YXZ, <ZXY (vertex is always in the middle), or <X (if it’s the only <X in the diagram).

Angles can also be named by a #. (<5)

5

There are 3 different <B’s in this diagram; therefore, none of them

should be called <B.

A

B

C

D<B ?

Angle Measurement

m<A means the “measure of <A”

Measure angles with a protractor.

Units of angle measurement are degrees (o).

Angles with the same measure are congruent angles.

If m<A = m<B, then <A <B.

Interior or Exterior?

B is ___________ C is ___________ D is ___________

in the interior

in the exterioron the <

A

B

C

D

Types of Angles Acute angle –

Right angle –

Obtuse angle –

Straight angle –

Measures between 0o & 90o

Measures exactly 90o

Measures between 90o & 180o

Measures exactly 180o

Ray Piece of a line with only one endpoint

(initial point) and continues forever in the other direction

Named by the endpoint and a second point named on the ray. (name MUST begin with the endpoint!)

AB

AB

Opposite Rays

2 rays that share a common initial point and face opposite directions.

QP and QS are opposite rays.P Q S

CONGRUENT ANGLES

Angles that have the same measure are congruent angles. Arcs on the figure also indicate which angles are congruent.

Practice

Example: 6 volunteers please!

Draw & label points A & B. Draw & label points C & D. Draw AB. Draw BC. Draw AC. Draw DA.

More Definitions Intersect –

2 or more figures intersect if they have one or more points in common.

Intersection – all points or sets of points the figures have in common

What is the intersection of:AB & DABC & ACBC & BC

WHEN 2 PLANES INTERSECT, THEIR INTERSECTION IS A

LINE.

Assignment