1

Geometric

Basics

PointsPoints• Points do not have actual size.

• How to Sketch:

Using dots

• How to label:

Use capital letters

Never name two points with the same letter in the same sketch.

2

A

BA

LinesLines• Extend indefinitely and have no thickness or width.• How to sketch : using arrows at both ends.

• How to name: 2 ways(1) small script letter

line n

(2) any two points on the line

• Never name a line using three points

, , , , ,AB BC AC BA CA CB������������������������������������������������������������������������������������������������������������������������������������������������ �����������

ABC�������������� �

3

n

AB

C

Collinear PointsCollinear Points

• Lie on the same line. (The line does not have to be visible).

4

A B C

A

B

C

Collinear

Non collinear

PlanesPlanes• Flat surface that extends indefinitely in all directions.

• How to sketch: Use a parallelogram (four sided figure)

• How to name: 2 ways

(1) Capital script letter

Plane M

(2) Any 3 non collinear points in the plane

Plane: ABC/ ACB / BAC / BCA / CAB / CBA

5

A

BC

Horizontal Plane

M

Vertical Plane Other

Different planes in a Different planes in a figure:figure:

6

A B

CD

EF

GH

Plane ABCD

Plane EFGH

Plane BCGF

Plane ADHE

Plane ABFE

Plane CDHG

Etc.

Other planes in the same Other planes in the same figure:figure:

Any three non collinear points determine a plane!

7

H

E

G

DC

BA

F

Plane AFGD

Plane ACGE

Plane ACH

Plane AGF

Plane BDG

Etc.

Coplanar ObjectsCoplanar Objects

Coplanar objects (points, lines, etc.) lie on the same plane. The plane does not have to be visible.

8

H

E

G

DC

BA

F

Are the following points coplanar?

A, B, C ?

A, B, C, F ?

H, G, F, E ?

E, H, C, B ?

A, G, F ?

C, B, F, H ?

Yes

No

Yes

Yes

Yes

No

SegmentSegment

9

Part of a line that consists of two points called the endpoints and all points between them.

How to sketch:

How to name:

Definition:

AB

AB or BA

The symbol AB is read as "segment AB".

AB (without a symbol) means the length of the segment or the distance between points A and B.

Congruent SegmentsCongruent Segments

Definition:

AB

D

C

Congruent segments can be marked with dashes.

Segments with equal lengths. (congruent symbol: )

RayRay

11

Definition:

( the symbol RA is read as “ray RA” )

How to sketch:

How to name:

R

A R A Y

RA ( not AR ) RA or RY ( not RAY )

RA : RA and all points Y such that A is between R and Y.

Opposite RaysOpposite Rays

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Definition:

( Opposite rays must have the same “endpoint” )

AX Y

D ED E

opposite rays not opposite rays

DE and ED are not opposite rays.

If A is between X and Y, AX and AY are opposite rays.

Intersection of FiguresIntersection of Figures

The intersection of two figures is the set of points that are common in both figures.

13

The intersection of two lines is a point.

m

n

P

Line m and line n intersect at point P.

3 Possibilities of Intersection of a3 Possibilities of Intersection of aLine and a PlaneLine and a Plane

(1) Line passes through plane – intersection is a point.

(2) Line lies on the plane - intersection is a line.

(3) Line is parallel to the plane - no common points.

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Intersection of Two Planes Intersection of Two Planes is a Line.is a Line.

AB�������������� �

15

P

R

A

B

Plane P and Plane R intersect at the line

16

Segment BisectorsSegment Bisectors

Any segment, line or plane that divides a segment into two congruent parts is called segment bisector.

Definition:

B

E

D

FA

BE

D

FA

E

D

A F

B

AB bisects DF. AB bisects DF.

AB bisects DF.Plane M bisects DF.

BetweenBetween

17

Definition: X is between A and B if AX + XB = AB.

A BX

AX + XB = AB AX + XB > AB

A BX

The Segment Addition The Segment Addition PostulatePostulate

AB

C

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

Postulate:

Example: If AC = x , CB = 2x and AB = 12, then, find x, AC and CB.

AC + CB = AB

x + 2x = 12

3x = 12

x = 4

2xx

12

x = 4AC = 4CB = 8

Step 1: Draw a figure

Step 2: Label fig. with given info.

Step 3: Write an equation

Step 4: Solve and find all the answers

You Try It!

Complete Practice Problemsand check your answers with

one another.