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74 Cards in this Set
- Front
- Back
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What is a simple curve?
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A curve that starts and stops without intersecting itself.
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What is simple closed curve?
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A simple curve that starts and stops at the same point
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What is the Jordan Curve Theorem?
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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.
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What is a plane region?
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A simple curve and its interior.
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What is a convex plane region?
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A plane region is convex if a line segment joining any two interior points is completely inside the curve.
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What is a concave plane region?
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A plane region that is not convex.
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What is a polygon?
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A closed curve created from the union of line segments.
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What is a polygonal region?
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The interior of the polygon.
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What are vertices?
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The endpoints of the line segments.
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What are sides?
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The line segments themselves.
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What are adjacent sides?
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Two sides of a polygon that share a common vertex.
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What are adjacent vertices?
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Two vertices that have a common side.
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What is a simple polygon?
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A polygon that has no sides intersecting.
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How is a polygon named?
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By the number of its sides. A polygon having n-sides is an n-gon.
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What is an exterior angle?
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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.
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What can we say about the two exterior angles at a vertex?
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They are congruent.
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What is the sum of the exterior angles of a convex polygon?
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360º
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How can we find the measure of an interior angle of a convex polygon?
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(n-2)180º
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What is an equilateral?
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A polygon with all sides congruent.
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What is an equilangular?
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A polygon with all interior angles congruent.
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What is a regular polygon?
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A polygon that is both equilateral and equiangular.
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What is a central angle?
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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.
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How do we find the measure of each interior angle in a regular polygon?
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[(n-2)180º]/n
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How do we find the measure of each exterior angle in a regular polygon?
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360º/n
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How do we find the measure of each central angle in a regular polygon?
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360º/n
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What type of polygon is a triangle?
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A 3-gon
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What is the median of a triangle?
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A segment from a vertex of a triangle to the midpoint of the side opposite that vertex.
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What is an altitude of a triangle?
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A line segment from a vertex that is perpendicular to a line containing the side opposide that vertex.
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What is an equilateral triangle?
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A triangle that has 3 equal sides. It is also equiangular.
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What is an isoceles triangle?
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A triangle that has 2 congruent sides. It also has 2 congruent angles.
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What is a scalene triangle
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A triangle that has no equal sides and no equal angles.
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What is a square?
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A quadrilateral that has all sides being congruent and all angles being 90º.
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What is a rectangle?
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A quadrilateral that has opposite sides being parallel and opposite sides being congruent. All angles are 90º
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What is a rhombus?
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A quadrilateral with all sides the same length and opposite sides being parallel
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What is a parallelogram?
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A quadrilateral with pairs of opposite sides being congruent and parallel.
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What is a kite?
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A quadrilateral will at least two pairs of adjacent sides being congruent; no side is used twice in forming the pairs.
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What is a trapezoid?
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A quadrilateral with one and only one pair of opposite sides being parallel.
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what is space?
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the set of all points that has no boundaries
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How does a plane partition space?
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A plane partitions space into three parts - the points on the plane, and two half-spaces
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What are the two ways that two planes can interact with each other?
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They are either parallel, or they intersect in a line
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What is the dihedral angle?
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The angle between two intersecting planes
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How do we measure the dihedral angle?
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We measure the angle whose sides lie in the plane and are perpendicular to the line of the intersection of the planes.
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How many ways can two lines intersect in space?
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three
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What are the three ways that two lines l and m can interact in space?
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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 |
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What are skew lines?
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Two lines that are not on the same plane and do not intersect.
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How many ways can a line and a plane interact?
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2
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What are the two ways a line and a plane can interact?
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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 |
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Wbat is a polyhedron?
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a collection of polygons joined to enclose a region of space
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What property do the polygons have when making up a polyhedra?
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Any two polygons have at most one side in common.
The enclosed region in space does not have any holes in it |
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What are the polygonal regions of the polyhedra called?
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Faces
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What is an edge?
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The line segments common to a pair of faces
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What is a vertex?
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The points of intersection of the edges
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What is a prism?
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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. |
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What is a Right Prism?
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When the lateral faces are all rectangular.
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What is an oblique prism?
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Wben the lateral faces of the prism are not all rectangular.
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How are prisms named?
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According to the type of polygons forming the bases and whether they are right or oblique.
Ex. Right Recangular Prism; Oblique Square Prism |
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Wbat is a pyramid?
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A polyhedron formed by connecting the vertices of a polygon to a point not in the plane of the polygon.
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What is the base of a pyramid?
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The polygon used to form the pyramid is the base.
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What shape are the lateral faces?
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The lateral faces are triangles
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What is the connecting point not in the plane of the polygon called?
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The apex (or vertex)
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What is a right pyramid?
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When the base of the pyramid is a regular polygon and the faces are concgruent isoceles triangles
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What is an oblique pyramid?
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A pyramid that does not have a regular polygon for a base with congruent isoceles triangles for the lateral faces
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What three properties does a regular polyhedron have?
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1. the surface is convex
2. the faces are congruent regular polygons 3. the same number of faces meet at each vertex |
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How many regular polygons are known?
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5
tetrahedron (3 faces), octahedron (5 faces), cube (6 faces), dodecahedron (12 faces), icosahedron (20 faces) |
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What is Euler's Formula?
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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
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How is a cylinder formed?
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From two simple closed curves, called bases, lyingin parallel planes with line segments joining corresponding points on the bases
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What is a right cylinder?
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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
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What is an oblique cylinder?
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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.
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What is a cone?
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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.
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What is a right circular cone?
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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
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What is an oblique circular cone?
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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
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What is a sphere?
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The set of all points that are the same distance from a fixed point, called the center
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What is a radius?
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A line segment joining the center to a point on the sphere
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What is the diameter?
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A line segment joining any two points on the sphere that also contains the center of the sphere
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