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MATH 301 > Exam 1 Topics > Flashcards

Exam 1 Topics Flashcards

1
Q

What do students learn at the Van Hiele level 0?

A

Geometric Recognition

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2
Q

What do students learn at the Van Hiele Level 1?

A

Geometric Analysis

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3
Q

What do students learn at the Van Hiele Level 2?

A

Geometric Relationships

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4
Q

A simple closed curve made up of line segments….

A

Polygon

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5
Q

a polygon where all angles are congruent (equiangular) and all sides are the same length (equilateral)…

A

Regular Polygon

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6
Q

Any polygon where a line segment joining any 2 points inside the polygon lies completely inside the polygon…

A

Convex Polygon

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7
Q

A polygon that is not convex; that is, there exists a line segment joining 2 points inside the polygon that does not lie completely inside the polygon…

A

Concave Polygon

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8
Q

A three sided polygon….

A

Triangle

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9
Q

A triangle in which all sides are of different lengths….

A

Scalene

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10
Q

A triangle in which at least 2 sides are the same length…

A

Isosceles

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11
Q

A triangle in which all 3 sides are the same length…

A

Equilateral

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12
Q

A four sided polygon…

A

Quadrilateral

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13
Q

A five sided polygon…

A

Pentagon

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14
Q

Define Square…

A

An equilateral parallelogram with all four angles equaling 90 degrees.

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15
Q

Define Rectangle…

A

A quadrilateral parallelogram in which 2 sets of opposite sides are parallel and all four angles equal 90 degrees.

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16
Q

Define Parallelogram…

A

A quadrilateral in which both sets of opposite sides are parallel.

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17
Q

Define Rhombus…

A

A quadrilateral in which all sides are the same length, one set of opposite angles must be acute while the other opposite angles must be obtuse. Exception: Square.

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18
Q

Deine Trapezoid…

A

A quadrilateral with exactly one set of parallel sides.

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19
Q

Define Kite…

A

A quadrilateral with exactly two pairs of congruent adjacent (consecutive) sides.

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20
Q

Define Kite…

A

A quadrilateral with exactly two pairs of congruent adjacent (consecutive) sides.

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21
Q

How do you find the measures of the vertex angles when given the number of sides?

A

(n-2) 180 / n

n minus 2 times 180 divided by n

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22
Q

How do you find the measures of the central angles or exterior angles when given the number of sides?

A

360 / n

360 divided by number of sides.

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23
Q

How do you find the number of sides when given the sum of all the vertex angles?

A
  1. ) (n-2) 180 = sum

2. ) Then solve for n.

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24
Q

How do you find the number of sides when given only one vertex angle measure?

A
  1. ) set angle measure equal to the equation (n-2)180 / n

2. ) Begin solving for n by multiplying n on both sides.

25
Q

How do you find the number of sides when given only a central angle?

A

360/n°

360 divided by the given central angle degree.

26
Q

How do you find the number of sides when given only an exterior angle?

A

360/n°

360 divided by the given central angle degree.

27
Q

How do you find the measures of the central angles when given the vertex angles?

A
  1. ) (n-2)180 / n = measure of vertex angle
  2. ) begin solving for n by multiplying n on both sides
  3. ) once number of sides is found, you can use the central angles shortcut, 360/n to find the degrees.
28
Q

How do you find the measures of the central angles when given the vertex angles?

A
  1. ) (n-2)180 / n = measure of vertex angle
  2. ) begin solving for n by multiplying n on both sides
  3. ) once number of sides is found, you can use the central angles shortcut, 360/n to find the degrees.
29
Q

How do you find all the lines of symmetry of a regular polygon?

A

Draw all the lines possible from opposite vertices ad all possible vertices to midpoints.

30
Q

How do you find rotational symmetry?

A

Use the Mira to mark lines of rotation (point) symmetry. Count rotations out of total number of sides. Example: 1/6 rotation would be 1/6 of 360 or 360/6.

31
Q

A line that is bound by two distinct end points, and contains every point on the line between its endpoints.

A

Segment

32
Q

A line with an endpoint that extends infinitely in one direction.

A

Ray

33
Q

An infinite number of points connected by a line that points infinitely in both directions.

A

Line

34
Q

Points lying on the same straight line….

A

colinear points

35
Q

Points lying on the same plane….

A

coplanar points

36
Q

Lines lying on the same plane….

A

coplanar lines

37
Q

Two lines that intersect to form a right angle…

A

perpendicular lines

38
Q

Two lines in the same plane that do not intersect…

A

parallel lines

39
Q

If two lines l and m are intersected by a third line, t, we call line t a(n) ___________.

A

Transversal

40
Q

The sum of two angles that measure to 90 degrees…

A

Complementary Angles

41
Q

The sum of two angles that measure 180 degrees….

A

Supplementary Angles

42
Q

Angles in the same position of the other grouping…

A

Corresponding Angles.

43
Q

Opposite angles formed by two intersecting lines…

A

Vertical Angles

44
Q

Angles that are inside the parallel lines…

A

Interior Angles

45
Q

Interior angles are on different sides of the transversal…

A

Alternate Interior Angles

46
Q

Angles above and below the parallel lines…

A

Exterior Angles

47
Q

Exterior angles are on different sides of the transversal…

A

Alternate Exterior Angles

48
Q

The polygonal regions of a polyhedron….

A

Face

49
Q

Line segments common to a pair of faces…

A

Edges

50
Q

The points of intersection of the edges…

A

Vertex

51
Q

When given the edges, faces, or vertices of a prism one can use Euler’s formula….

A

F + V - 2 = E or F + V = E - 2

52
Q

For an n-gon prism in Euler’s formula the F can be found by…..

A

n + 2

53
Q

For an n-gon prism in Euler’s fomula the V can be found by…

A

2n

54
Q

For an n-gon prism in Euler’s fomula the F + V can be found by.

A

3n + 2

55
Q

For an n-gon prism in Euler’s fomula the E can be found by…

A

3n

56
Q

For an n-gon Pyramid in Euler’s fomula the F can be found by….

A

n + 1

57
Q

For an n-gon prism in Euler’s fomula the V can also be found by….

A

n + 1

58
Q

For an n-gon prism in Euler’s fomula the F + V can be found by….

A

2n + 2

59
Q

For an n-gon prism in Euler’s fomula the E can be found by…

A

2n

MATH 301 (23 decks)

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