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# MA308 Test 2

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

Question | Answer |
---|---|

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