Beat the Computer! Geometry Vocabulary and Formulas for Unit 1

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Presentation transcript:

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

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 inductive reasoning Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

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

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

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

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

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

P point: a location in space having no size Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

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

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

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 collinear points Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

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

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

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

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

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

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

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

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

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

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 opposite rays Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 parallel lines Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 skew lines Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 parallel planes Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

congruent () segments Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

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

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

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

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 acute angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 right angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 obtuse angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 straight angle Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 congruent angles Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 perpendicular lines Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

perpendicular bisector of a segment Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 angle bisector Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 distance formula Chris Giovanello, LBUSD Math Curriculum Office, 2004

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

Chris Giovanello, LBUSD Math Curriculum Office, 2004 midpoint formula Chris Giovanello, LBUSD Math Curriculum Office, 2004

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