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