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74 Cards in this Set

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  • Back
What is a simple curve?
A curve that starts and stops without intersecting itself.
What is simple closed curve?
A simple curve that starts and stops at the same point
What is the Jordan Curve Theorem?
Every simple closed curve divides the plane into three disjoint sets: the points on the curve, the points in the interior of the curve and the points in the exterior.
What is a plane region?
A simple curve and its interior.
What is a convex plane region?
A plane region is convex if a line segment joining any two interior points is completely inside the curve.
What is a concave plane region?
A plane region that is not convex.
What is a polygon?
A closed curve created from the union of line segments.
What is a polygonal region?
The interior of the polygon.
What are vertices?
The endpoints of the line segments.
What are sides?
The line segments themselves.
What are adjacent sides?
Two sides of a polygon that share a common vertex.
What are adjacent vertices?
Two vertices that have a common side.
What is a simple polygon?
A polygon that has no sides intersecting.
How is a polygon named?
By the number of its sides. A polygon having n-sides is an n-gon.
What is an exterior angle?
It is formed by two sides of the polygon that have a common vertex. If we extend a line segment at a vertex, we form an exterior angle.
What can we say about the two exterior angles at a vertex?
They are congruent.
What is the sum of the exterior angles of a convex polygon?
How can we find the measure of an interior angle of a convex polygon?
What is an equilateral?
A polygon with all sides congruent.
What is an equilangular?
A polygon with all interior angles congruent.
What is a regular polygon?
A polygon that is both equilateral and equiangular.
What is a central angle?
A central angle is formed by putting a vertex at the center of a regular polygon and joining this vertex to adjacent vertices of the polygon.
How do we find the measure of each interior angle in a regular polygon?
How do we find the measure of each exterior angle in a regular polygon?
How do we find the measure of each central angle in a regular polygon?
What type of polygon is a triangle?
A 3-gon
What is the median of a triangle?
A segment from a vertex of a triangle to the midpoint of the side opposite that vertex.
What is an altitude of a triangle?
A line segment from a vertex that is perpendicular to a line containing the side opposide that vertex.
What is an equilateral triangle?
A triangle that has 3 equal sides. It is also equiangular.
What is an isoceles triangle?
A triangle that has 2 congruent sides. It also has 2 congruent angles.
What is a scalene triangle
A triangle that has no equal sides and no equal angles.
What is a square?
A quadrilateral that has all sides being congruent and all angles being 90º.
What is a rectangle?
A quadrilateral that has opposite sides being parallel and opposite sides being congruent. All angles are 90º
What is a rhombus?
A quadrilateral with all sides the same length and opposite sides being parallel
What is a parallelogram?
A quadrilateral with pairs of opposite sides being congruent and parallel.
What is a kite?
A quadrilateral will at least two pairs of adjacent sides being congruent; no side is used twice in forming the pairs.
What is a trapezoid?
A quadrilateral with one and only one pair of opposite sides being parallel.
what is space?
the set of all points that has no boundaries
How does a plane partition space?
A plane partitions space into three parts - the points on the plane, and two half-spaces
What are the two ways that two planes can interact with each other?
They are either parallel, or they intersect in a line
What is the dihedral angle?
The angle between two intersecting planes
How do we measure the dihedral angle?
We measure the angle whose sides lie in the plane and are perpendicular to the line of the intersection of the planes.
How many ways can two lines intersect in space?
What are the three ways that two lines l and m can interact in space?
1. l and m can intersect
2. l and m can be parallel and on the same plane
3. l and m can be skew lines
What are skew lines?
Two lines that are not on the same plane and do not intersect.
How many ways can a line and a plane interact?
What are the two ways a line and a plane can interact?
1. The line l is parallel to plane P if l does not intersect P

2. The line m is perpendicular to a plane Q at point K if m is perpendicular to every line in the plane Q that contains K
Wbat is a polyhedron?
a collection of polygons joined to enclose a region of space
What property do the polygons have when making up a polyhedra?
Any two polygons have at most one side in common.

The enclosed region in space does not have any holes in it
What are the polygonal regions of the polyhedra called?
What is an edge?
The line segments common to a pair of faces
What is a vertex?
The points of intersection of the edges
What is a prism?
A polyhedron with a pair of congruent faces, called bases, that lie in parallel planes.

The vertices of the bases are joined to form parallelogram shaped lateral faces of the prism.
What is a Right Prism?
When the lateral faces are all rectangular.
What is an oblique prism?
Wben the lateral faces of the prism are not all rectangular.
How are prisms named?
According to the type of polygons forming the bases and whether they are right or oblique.

Ex. Right Recangular Prism; Oblique Square Prism
Wbat is a pyramid?
A polyhedron formed by connecting the vertices of a polygon to a point not in the plane of the polygon.
What is the base of a pyramid?
The polygon used to form the pyramid is the base.
What shape are the lateral faces?
The lateral faces are triangles
What is the connecting point not in the plane of the polygon called?
The apex (or vertex)
What is a right pyramid?
When the base of the pyramid is a regular polygon and the faces are concgruent isoceles triangles
What is an oblique pyramid?
A pyramid that does not have a regular polygon for a base with congruent isoceles triangles for the lateral faces
What three properties does a regular polyhedron have?
1. the surface is convex
2. the faces are congruent regular polygons
3. the same number of faces meet at each vertex
How many regular polygons are known?

tetrahedron (3 faces), octahedron (5 faces),
cube (6 faces),
dodecahedron (12 faces), icosahedron (20 faces)
What is Euler's Formula?
For any given polyhedra, let F=the number of faces, V=the number of vertices and E=the number of edges then F+V=E+2
How is a cylinder formed?
From two simple closed curves, called bases, lyingin parallel planes with line segments joining corresponding points on the bases
What is a right cylinder?
At cylinder that has the property that a line segment AB connectiong a point A on a base to its corresponding point B on the other base is perpendicular to the planes containing the bases
What is an oblique cylinder?
A cylinder that has the property that the bases are parallel bu line segments connecting corresponding points are not perpendicular to the planes containing the bases.
What is a cone?
The union of the interior of a simple closed curve and all line swgments joining points on the curve to a point, called the apex or vertex, that is not in the plane of the curve.
What is a right circular cone?
A cone that has the property that the line segment from the apex of the cone to the center of the circular base is perpendicular to the plane containing the base
What is an oblique circular cone?
A cone that has the property that the line segment connecting the apex to the base is not perpendicular to the plane containing the base
What is a sphere?
The set of all points that are the same distance from a fixed point, called the center
What is a radius?
A line segment joining the center to a point on the sphere
What is the diameter?
A line segment joining any two points on the sphere that also contains the center of the sphere