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MA308 Test 2

Mathematics for the Elementary/Middle School Teachers II - Test Two

What are the fundamental building blocks of geometry? Points, Lines, and Planes
Define Collinear Collinear refers to points on the same line.
Define Plane A plane is a flat surface which extends and contains lines.
Define Skew Lines Skew lines are lines that do not lie on the same place in space, they cannot be parallel or intersect.
Define Intersecting Lines Intersecting lines are lines that cross each other at some point.
Define Parallel Lines Parallel lines are lines that have no points in common but share the same slope.
Define Axiom An axiiom is something we assume to be true without proof.
Find the number of lines that can be drawn through a certain number of points. n(n-1)/2 Number of points multiplied by the number of points minus 1, divided by 2.
Acute Angle Less than 90 degrees
Right Angle Measures exactly 90 degrees
Obtuse Angle Measures great than 90 degrees
Straight Angle Measures exactly 180 degrees
Define Perpendicular Planes Perpendicular planes are two planes which are perpendicular to one another and whose angle measures 90 dgrees.
Define Dihedral Angles Dihedral Angles are formed by the union of two half-planes.
Define Simple Curves Simples curves do not intersect themselves.
Define Closed Curves Closed curves can be drawn by starting and stopping at the same point.
Define Polygons Polygons are simple closed curves with sides that are only segments.
Define Convex Curves Convex curves are simple and closed such that the segmebt connecting any two points in the interior of the curve is wholly contained the the interior of the curve.
Define Concave Curves Concave curves are simple closed and not convex.
What is a polygon region? A polygon and its interior makes up a polygon region.
How are polygons classified? According to the number of sides or vertices that they have.
A polygon with 4 sides Quadrilateral
A polygon with 7 sides Heptagon
A polygon with n sides N-gon
Define Interior Angle Interior angles are determined by two sides of a convex polygon having a common vertex.
Define Exterior Angle Exterior angles are determined by a side of the polygon and the extension of a continuous side of the polygon.
Define Vertex A vertex is the point where two segements meet.
Define Diagnonal A diagonal is a line segement connecting nonconsecutive vertices of a polygon.
Define Equilateral Equilateral means all sides of the shape are of equal length.
Define Equilangular Equilangular means all angles of the shape are of equal measure.
What is a regular polygon? A regular polygon is a polygon that is both equilateral and equilangular.
Right Triangle Contains exactly one right angle.
Acute Triangle All angles are acute.
Obtuse Triangle Contains exactly one obtuse angle.
Scalene Triangle No congruent sides
Isosceles Triangle At least two congruent sides
Equilateral Triangle All sides are equil (equilateral)
Trapezoid A polygon with at least one pair of parallel lines.
Kite A polygon with two adjacent sides congruent and two other sides congruent.
Isosceles Trapezoid A polygon with congruent base angles.
Parallelogram A polygon in which each pair of opposite sides is parallel.
Rectangle A parallelogram with a right angle.
Rhombus A parallelogram with two adjacent sides that are congruent.
Square A rectangle with two adjacent sides that are congruent.
Define Vertical Angles Vertical angles are a pair of angles directly opposite each other that are equal in measurement.
Define Complementary Angles Complementary angles are two angles whose sum measures 90 degrees.
Define Supplementary Angles Supplementary angles are two angles whose sum meansures 180 degrees.
Define Transversal A transversal is any line that intersects a pair of lines in a plane.
Define Alternate Interior Angles Alternate interior angles are congruent angles within the interior which are not on the same line.
Define Corresponding Angles Corresponding angles are congruent angles which are found in the same position of different lines.
Define Alternate Exterior Angles Alternate Exterior Angles are congruent angles within the exterior which are not on the same line.
Angles and Parallel Lines Property If any two distinct coplanar lines are cut by a transversal, then a pair of corresponding angles, alternate interior angles, or alternate exterior angles are congruent if and only if the lines are parallel.
Inductive Reasoning Inductive reasoning is based on observations.
Deductive Reasoning Deductive reasoning is based on given information.
Interior Angles of a Triangle The sum of the Interior Angles of a Triangle always equal 180 degrees.
What is a simple closed surface? A simple closed surface has exactly one interior, has no holes, and is hollow.
Sphere The set of all points at a given distance from a given point, the center.
Center A point in the exact middle of a figure from which all lines have equal length.
Solid The set of all closed surface points on a simple closed surface with all interior points.
Polyhedron A simple closed surface made up of polygons regions or faces.
Vertices A point where two ray, sides, or edges meet. Alsom the point at the top of a cone.
Edges The sides of a polygon or line segement where two faces of a solid figure meet.
Prism A polyhedron in which two congruent faces lie in parallel planes and the other faces are bound by parallelograms.
Base The bottom line or face shape of an object or solid.
Lateral Face The faces of a prism other than the bases.
Right Prism The lateral faces of a prism are all bound by rectangles.
Oblique Prism Some of the lateral faces are not bounded by rectangles.
Pyramid A polyhedron which is determined by a polygon and a point not in the plane of the polygon.
Apex The highest point or the point at the top of a shape.
Right Pyramid All the lateral faces of the pyramid are congruent isosceles triangles.
Name the platonic solids. Cube, Tetrahedron, Octahedron, Dodecahedron, Icosahedron
Cylinder A solid shape with one curved surface and two congruent circular or elliptical bases.
Circular Cylinder A cylinder whose base is a circular region.
Right Cylinder Contains a line segment forming a circular cylinder that is perpendicular to the bases.
Oblique Cylinder A circular cylinder that is not a right cylinder.
Cone A solid shape with an elliptical or circular base and a curved surface that tapers to a point (vertex).
Right Circular Cone A cone whose altitude intersects the base at the center of the circle.
Oblique Circular Cone A cone whose altitude intersects the base at an angle to the center of the cone.
What is the difference between similar and congruent objects? Similar objects have the same shape while congruent have the same shape and the same size.
Define Arc An arc is any part of a circle that can be drawn without lifting a pencil.
What is the Side Side Side Property? If three sides of one triangle are congruent to three sides of the second triangle then the triangles are congruent.
What is the triangle inequality? The sum of the measures of any two sides of a triable must be greater than the measure of the third side. (A+B>C)
What is the Side Angle Side Property? If two sides and an angle of two triangles are congruent then the triangles are congruent.
What is the Angle Side Angle Property? Two triangles are congruent if they have angles and an included side which are congruent.
What is the Angle Angle Side Property? Two triangles are congruent if they have two angles and a side opposite one of the angles which are congruent.
What is a scale factor? The ratio of the corresponding side lengths.
What is the Angle Angle Property? If two angles of one triangle are congruent to two angles of a second triangle then the triangles are similar.
What is a midsegment? A midsegment is the segment connecting the midpoints of two sides of a triangle or two adjacent sides of a quidrilateral.
What is indirect measurement? Using ratios to determine a measurement and not actually measuring.
Descibe a shape that is equilangular but not equilateral. A Rectangle
Describe a shape that is equilateral but not equilangular. A Rhombus
True/False - A parallelogram has 4 acute angles. False - A parallelogram can have four right angles. Otherwise there must be two acute and two obtuse angles.
True/False - A line segment contains an infinite number of points. True - There are an infinite number of points on a line segment.
True/False - The union of two rays is always a line. False - Whne two rays are combined at the end point, they may form a line if extended in opposite directions or they will form other shapes.
True/False - Every equilateral triangle is an acute triangle. True - All angles in an equilateral triangle will be the same so they will be acute.
True/False - All rectangles are similar. False
Find the number of diagonals in a polyggon. x(x-3)/2 Number of sides multiplied by the number of sides minus three and then divided by two.
Find the measures of the angles of a n-gon. (n-2)180/n Number of sides minus two, multiplied by 180 degrees then divided by the number of sides.
Where do all the points in space equidistant from a given point lie? The points lie on a sphere.
Find the number of one-to-one correspondences can be listed between vertices. (n)(n-1)(n-2)(n-3)...(1) = n!
True/False - A square is a rhombus. True
True/False - All squares are trapezoids. True - All squares by definition are trapezoids.
Created by: bschult3