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

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Presentation on theme: "Chris Giovanello, LBUSD Math Curriculum Office, 2004 Beat the Computer! Geometry Vocabulary and Formulas for Unit 1."— Presentation transcript:

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

3 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

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

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

6 Chris Giovanello, LBUSD Math Curriculum Office, 2004 conjecture

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

8 Chris Giovanello, LBUSD Math Curriculum Office, 2004 counterexample

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

10 Chris Giovanello, LBUSD Math Curriculum Office, 2004 point

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

12 Chris Giovanello, LBUSD Math Curriculum Office, 2004 space

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

14 Chris Giovanello, LBUSD Math Curriculum Office, 2004 line

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

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

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

18 Chris Giovanello, LBUSD Math Curriculum Office, 2004 plane

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

20 Chris Giovanello, LBUSD Math Curriculum Office, 2004 coplanar

21 Chris Giovanello, LBUSD Math Curriculum Office, 2004 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

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

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

24 Chris Giovanello, LBUSD Math Curriculum Office, 2004 segment

25 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

26 Chris Giovanello, LBUSD Math Curriculum Office, 2004 ray

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

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

29 Chris Giovanello, LBUSD Math Curriculum Office, 2004 opposite rays: two collinear rays with the same endpoint XSR and are opposite rays

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

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

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

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

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

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

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

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

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

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

40 Chris Giovanello, LBUSD Math Curriculum Office, 2004 angle

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

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

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

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

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

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

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

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

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

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

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

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

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

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

55 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

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

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

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

59 Chris Giovanello, LBUSD Math Curriculum Office, 2004 distance formula: the distance d between two points A(x 1,x 2 ) and B(y 1,y 2 ):

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

61 Chris Giovanello, LBUSD Math Curriculum Office, 2004 midpoint formula: the coordinates of the midpoint M of AB with endpoints A(x 1,x 2 ) and B(y 1,y 2 ) are:


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