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**Beat the Computer! Geometry Vocabulary and Formulas for Unit 1**

Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

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 Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

inductive reasoning Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**reasoning based on patterns you observe**

inductive reasoning: reasoning based on patterns you observe Using the pattern, what is the next term in the sequence? Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

conjecture Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**a conclusion reached when using inductive reasoning**

conjecture: a conclusion reached when using inductive reasoning “Based on the pattern, I think the answer is…” Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

counterexample Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**an example for which a conjecture is false**

counterexample: an example for which a conjecture is false Conjecture: All integers are natural numbers. Counterexample: -1 Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

point Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**P point: a location in space having no size**

Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

space Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

space: the set of all points Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

line Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**a series of points that extends in two opposite directions without end**

line: a series of points that extends in two opposite directions without end t P Q line t or or Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

collinear points Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**points that lie on the same line**

collinear points: points that lie on the same line collinear non-collinear X Y Line l Z Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

plane Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**a flat surface that has no thickness**

plane: a flat surface that has no thickness P Plane P C B A Plane ABC Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

coplanar Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**points and lines that lie in the same plane**

coplanar: points and lines that lie in the same plane X coplanar Y Line l Line m X Y non-coplanar Line l Line m Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

postulate or axiom Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**a statement that is accepted as true without proof**

postulate or axiom: a statement that is accepted as true without proof Example: Through any two points there is exactly one line. Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

segment Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

segment: the part of a line consisting of two endpoints and all the points between them A B endpoint Segment AB Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

ray Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

ray: the part of a line consisting of two endpoints and all the points between them Ray YX X Y endpoint Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

opposite rays Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**two collinear rays with the same endpoint**

opposite rays: two collinear rays with the same endpoint X R S and are opposite rays Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

parallel lines Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**coplanar lines that do not intersect**

parallel lines: coplanar lines that do not intersect Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

skew lines Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**lines that do not lie in the same plane**

skew lines: lines that do not lie in the same plane Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

parallel planes Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**planes that do not intersect**

parallel planes: planes that do not intersect A G F E D C B H Plane ABCD is parallel to Plane EFGH Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**congruent () segments**

Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**segments with the same length**

congruent segments: segments with the same length A B C D 5 cm AB = CD Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

midpoint of a segment Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**a point that divides a segment into two congruent segments**

midpoint of a segment: a point that divides a segment into two congruent segments A B C Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**two rays with the same endpoint**

angle: two rays with the same endpoint vertex Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

acute angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**an angle whose measure is between 0º and 90º**

acute angle: an angle whose measure is between 0º and 90º Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

right angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**an angle whose measure is exactly 90º**

right angle: an angle whose measure is exactly 90º Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

obtuse angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**an angle whose measure is between 90º and 180º**

obtuse angle: an angle whose measure is between 90º and 180º Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

straight angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**an angle whose measure is exactly 180º**

straight angle: an angle whose measure is exactly 180º Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

congruent angles Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**angles with the same measure**

congruent angles: angles with the same measure Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

perpendicular lines Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**two lines that intersect to form right angles**

perpendicular lines: two lines that intersect to form right angles Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**perpendicular bisector of a segment**

Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**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 Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

angle bisector Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**a ray that divides an angle into two congruent coplanar angles**

angle bisector: a ray that divides an angle into two congruent coplanar angles Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

distance formula Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**the distance d between two points A(x1,x2) and B(y1,y2):**

distance formula: the distance d between two points A(x1,x2) and B(y1,y2): Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

midpoint formula Chris Giovanello, LBUSD Math Curriculum Office, 2004

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**Chris Giovanello, LBUSD Math Curriculum Office, 2004**

midpoint formula: the coordinates of the midpoint M of AB with endpoints A(x1,x2) and B(y1,y2) are: Chris Giovanello, LBUSD Math Curriculum Office, 2004

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Objectives: To use inductive reasoning to make conjectures.

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