Chris Giovanello, LBUSD Math Curriculum Office, 2004 Beat the Computer! Geometry Vocabulary and Formulas for Unit 1

Chris Giovanello, LBUSD Math Curriculum Office, 2004

Beat the Computer!Geometry

Vocabulary and

Formulas for Unit 1


Directions:•A slide will appear with a term

•Say the definition aloud before the computer can answer (5 sec.)

•You will hear a sound when the slide changes


inductive reasoning


inductive reasoning:

reasoning based on patterns you

observeUsing the pattern, what is the next term in the sequence?


conjecture


conjecture:

a conclusion reached when using inductive reasoning

“Based on the pattern, I think the answer is…”


counterexample


counterexample:

an example for which a conjecture

is falseConjecture: All integers are natural numbers.

Counterexample: -1


point


point:

a location in space having no size

P


space


space:

the set of all points


line


line:

a series of points that extends in two

opposite directions without endP

Qt

line t or PQ or QP


collinear points


collinear points:

points that lie on the same line

collinear non-collinear

XY

Line

l

Z

X

Y

Line

l

Z


plane


plane:

a flat surface that has no thickness

P

Plane P

C

B

A

Plane ABC


coplanar


coplanar:

points and lines that lie in the same plane

X

coplanar

Y Line l

Line m

XY

non-coplanarLi

ne l

Line m


postulateor

axiom


postulate or axiom:

a statement that is accepted as true

without proof

Example: Through any two points there is exactly one line.


segment


segment:

the part of a line consisting of two

endpoints and all the points between them

A Bendpoint endpoint

Segment AB


ray


ray:

the part of a line consisting of two

endpoints and all the points between them

X Y endpoint

Ray YX


opposite rays


opposite rays:

two collinear rays with the same endpoint

X SR

and are opposite raysRQ RS


parallel lines


parallel lines:

coplanar lines that do not intersect


skew lines


skew lines:

lines that do not lie in the same plane


parallel planes


parallel planes:

planes that do not intersect

A

G

FE

D C

B

H

Plane ABCD is parallel to Plane

EFGH


congruent () segments


congruent segments:

segments with the same length

A B

C D

A B

C D

5 cm

5 cm

AB = CD

AB = CD


midpoint of a segment


midpoint of a segment:

a point that divides a segment into two

congruent segments

A B C

BCAB


angle


angle:

two rays with the same endpoint

vertex


acute angle


acute angle:

an angle whose measure is between 0º

and 90º


right angle


right angle:

an angle whose measure is exactly 90º


obtuse angle


obtuse angle:

an angle whose measure is between

90º and 180º


straight angle


straight angle:

an angle whose measure is exactly

180º


congruent angles


congruent angles:

angles with the same measure


perpendicular lines


perpendicular lines:

two lines that intersect to form right angles


perpendicular bisector of a

segment


perpendicular bisector of a segment:

a line, segment, or ray that is to the segment at its midpoint, thereby bisecting the segment

into two segments


angle bisector


angle bisector:

a ray that divides an angle into two congruent

coplanar angles


distance formula


distance formula:

the distance d between two points A(x1,x2) and

B(y1,y2):2

122

12 )()( yyxxd


midpoint formula


midpoint formula:

the coordinates of the midpoint M of AB with endpoints A(x1,x2) and

B(y1,y2) are:

2,

22121 yyxx

M

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Chris Giovanello, LBUSD Math Curriculum Office, 2004 Beat the Computer! Geometry Vocabulary and Formulas for Unit 1