MODERN GEOMETRY Section 2.1

Thompson

A

POINT

“That which has no part”

• Has no size

• Denoted by capital

letter

• Location on plane

A D

LINE

“Breadthless length”

• Has no width

• Infinite length of

“connected” points

• Represented with two

arrows

• Say: “Line AD”

• Write: AD

• Each line contains at least two distinct points

• Any two points contain one and only one

line

• Points that lie on the same line are said to

be collinear

A

B

D

G

RAY

“Breadthless length”

• Has no width

• Infinite length of “connected”

points, with starting point

• Represented with one arrow

• Say: “Ray GB”

• Write:

• Starting point matters

GB

A

B C

D

G

SEGMENT

“Breadthless length”

• Has no width

• Fixed length of “connected”

points, with starting/ending

point

• Represented with no arrows

• Say: “Segment GC”

• Write: GC

ANGLES

“measure of distance”

• Lines meeting at a common

endpoint

• We call this sides and vertex

(pl. vertices)

• Need three points to name

• Say: “Angle AGB or Angle

BGA”

• Write: BGAorAGB

A

B C

D

G

*Vertex is the middle point

GABAGB

ANGLES

Protractor Postulate

• Basically “we’re allowed

to measure angles with a

protractor”

• We’ll start with degrees

• Line up one side with 0°

or 180 °

• So, m∠𝐴𝐺𝐵= 77°

A

B C

D

G

ANGLES

Types of Angles

• Right – 90°

• Perpendicular

• Write: 𝐺𝐶 ⊥ 𝐺𝐸

• Acute – between 0° and 90°

• Obtuse – between 90° and 180°

• Straight – 180°

• Reflex – between 180° and 360°

A

B C

D

G

E

54°

ANGLES

Congruent Angles

• Have the same measure

• Say: “angle BGC is

congruent to angle AGF”

• Write:

• Notate using “little arcs”

A

B C

D

G

E

54°

AGFBGC

F

ANGLES

Adjacent Angles

• Share common side and

vertex

• Say: “angle BGC is

adjacent to angle CGD”

A

B C

D

G

E

54°

F

ANGLES

Angle Addition Postulate

• Smaller adjacent angles

must sum to the whole

angle

• Can find unknown angles

by setting up algebra

equations

• Find m∠DGE, etc.

A

B C

D

G

E

54°

F

77°

ANGLES

Angle Pairs

• Complementary – Angles

whose measures sum to 90°

• Supplementary – Angles

whose measures sum to 180°

A

B C

D

G

E

54°

F

77°

CIRCLES

The set of all points equidistant

from a given point

• Center point

• Say: “Circle C”

• Radius = ½ Diameter

• Chord

• Tangent

C

rD

E

FA

B

POLYGONS

A simple, closed curve of line

segments

• Named by its vertices

• Have adjacent sides, and

adjacent angles

• Congruent sides marked with

hash mark(s)

A

B

C

E D

POLYGONS

Type of Polygon / # sides

• Triangle 3

• Quadrilateral 4

• Pentagon 5

• Hexagon 6

• Octogon 8

• Decagon 10

• n – gon n

POLYGONS

Regular Polygon

• All sides and angles are

congruent

TRIANGLES

Characterized by sides or angles

• Write as ΔABC

• Interior angle sum

• ∠A + ∠B + ∠C = 180°

A

B C

TRIANGLES

Classifying…

• By Sides

• By Angles

QUADRILATERALS

Characterized by their sides,

angles, and parallel lines

• Parallel lines are in the same

plane and do not intersect

• Parallel lines can be marked

with “arrows”

QUADRILATERALSSQUARE

All sides congruent, all angles

are right.

QUADRILATERALSRECTANGLES

All angles are right.

QUADRILATERALSRHOMBUS

All sides are congruent

QUADRILATERALSPARALLELOGRAM

Opposite sides are parallel

QUADRILATERALSTRAPEZOID

Exactly on pair of sides is

parallel

QUADRILATERALSKITE

Two pairs of adjacent and

congruent sides

QUADRILATERALS

SYMMETRY

Reflection Symmetry

• An imaginary line such that

the figure can be folded

exactly unto itself

SYMMETRY

Rotational Symmetry

• If shape is identical even if

turned less than full rotation

CLASSWORK / HOMEWORK

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