Exam 1 Topics Flashcards
What do students learn at the Van Hiele level 0?
Geometric Recognition
What do students learn at the Van Hiele Level 1?
Geometric Analysis
What do students learn at the Van Hiele Level 2?
Geometric Relationships
A simple closed curve made up of line segments….
Polygon
a polygon where all angles are congruent (equiangular) and all sides are the same length (equilateral)…
Regular Polygon
Any polygon where a line segment joining any 2 points inside the polygon lies completely inside the polygon…
Convex Polygon
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…
Concave Polygon
A three sided polygon….
Triangle
A triangle in which all sides are of different lengths….
Scalene
A triangle in which at least 2 sides are the same length…
Isosceles
A triangle in which all 3 sides are the same length…
Equilateral
A four sided polygon…
Quadrilateral
A five sided polygon…
Pentagon
Define Square…
An equilateral parallelogram with all four angles equaling 90 degrees.
Define Rectangle…
A quadrilateral parallelogram in which 2 sets of opposite sides are parallel and all four angles equal 90 degrees.
Define Parallelogram…
A quadrilateral in which both sets of opposite sides are parallel.
Define Rhombus…
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.
Deine Trapezoid…
A quadrilateral with exactly one set of parallel sides.
Define Kite…
A quadrilateral with exactly two pairs of congruent adjacent (consecutive) sides.
Define Kite…
A quadrilateral with exactly two pairs of congruent adjacent (consecutive) sides.
How do you find the measures of the vertex angles when given the number of sides?
(n-2) 180 / n
n minus 2 times 180 divided by n
How do you find the measures of the central angles or exterior angles when given the number of sides?
360 / n
360 divided by number of sides.
How do you find the number of sides when given the sum of all the vertex angles?
- ) (n-2) 180 = sum
2. ) Then solve for n.
How do you find the number of sides when given only one vertex angle measure?
- ) set angle measure equal to the equation (n-2)180 / n
2. ) Begin solving for n by multiplying n on both sides.
How do you find the number of sides when given only a central angle?
360/n°
360 divided by the given central angle degree.
How do you find the number of sides when given only an exterior angle?
360/n°
360 divided by the given central angle degree.
How do you find the measures of the central angles when given the vertex angles?
- ) (n-2)180 / n = measure of vertex angle
- ) begin solving for n by multiplying n on both sides
- ) once number of sides is found, you can use the central angles shortcut, 360/n to find the degrees.
How do you find the measures of the central angles when given the vertex angles?
- ) (n-2)180 / n = measure of vertex angle
- ) begin solving for n by multiplying n on both sides
- ) once number of sides is found, you can use the central angles shortcut, 360/n to find the degrees.
How do you find all the lines of symmetry of a regular polygon?
Draw all the lines possible from opposite vertices ad all possible vertices to midpoints.
How do you find rotational symmetry?
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.
A line that is bound by two distinct end points, and contains every point on the line between its endpoints.
Segment
A line with an endpoint that extends infinitely in one direction.
Ray
An infinite number of points connected by a line that points infinitely in both directions.
Line
Points lying on the same straight line….
colinear points
Points lying on the same plane….
coplanar points
Lines lying on the same plane….
coplanar lines
Two lines that intersect to form a right angle…
perpendicular lines
Two lines in the same plane that do not intersect…
parallel lines
If two lines l and m are intersected by a third line, t, we call line t a(n) ___________.
Transversal
The sum of two angles that measure to 90 degrees…
Complementary Angles
The sum of two angles that measure 180 degrees….
Supplementary Angles
Angles in the same position of the other grouping…
Corresponding Angles.
Opposite angles formed by two intersecting lines…
Vertical Angles
Angles that are inside the parallel lines…
Interior Angles
Interior angles are on different sides of the transversal…
Alternate Interior Angles
Angles above and below the parallel lines…
Exterior Angles
Exterior angles are on different sides of the transversal…
Alternate Exterior Angles
The polygonal regions of a polyhedron….
Face
Line segments common to a pair of faces…
Edges
The points of intersection of the edges…
Vertex
When given the edges, faces, or vertices of a prism one can use Euler’s formula….
F + V - 2 = E or F + V = E - 2
For an n-gon prism in Euler’s formula the F can be found by…..
n + 2
For an n-gon prism in Euler’s fomula the V can be found by…
2n
For an n-gon prism in Euler’s fomula the F + V can be found by.
3n + 2
For an n-gon prism in Euler’s fomula the E can be found by…
3n
For an n-gon Pyramid in Euler’s fomula the F can be found by….
n + 1
For an n-gon prism in Euler’s fomula the V can also be found by….
n + 1
For an n-gon prism in Euler’s fomula the F + V can be found by….
2n + 2
For an n-gon prism in Euler’s fomula the E can be found by…
2n
