Review Sheet 3   Math 106

 

New material after midterm 2 is in bold italic.  The final exam is comprehensive over the whole quarter.

Know the meaning of

    (Cartesian) coordinate system

    slope of a line

   point, line, plane

    ray

    line segment

    vertices of a triangle or other polygon

    sides of a triangle or other polygon

    types of triangles: equilateral, isosceles, obtuse scalene, right, acute

    perpendicular lines, perpendicular line segments

    types of quadrilaterals:  rectangle, square, parallelogram, trapezoid, rhombus

    geometric figure

    congruence between two geometric figures

    symmetry of a geometric figure

    curve, closed curve, simple closed curve

    collinear points

    vertex of an angle

    sides of an angle

    measurement of angles using degrees

    measurement of angles using radians

    parallel lines

    transversal to parallel lines

    alternate interior angles formed by a transversal

    corresponding angles formed by a transversal

    vertical angles (associated with two intersecting lines)

    regular polygon

    skew lines

    parallel planes

    sphere, cylinder, prism, cone, pyramid


    unit area


   
area and perimeter

    circumference of a circle

    volume and surface area


    Pythagorean theorem


    congruence and similarity of triangles and other figures


    the trigonometric ratios: sin, cos, tan

Formal Definitions

    triangle

    right angle

    quadrilateral

    parallel lines

    angle

 

Basic Properties of Geometry


    through two distinct points there is a unique line

    the triangle inequality

    the parallel postulate

    the sum of the measures of the three angles of a triangle is  180º

    measures of a pair of vertical angles are equal

    alternate interior angles formed by a transversal to parallel lines are congruent
   
    corresponding angles formed by a transversal to parallel lines are congruent

    given any three noncollinear points, there is a unique plane through all three.

    the intersection of any two distinct planes which intersect at all is a line

    if  A  and  B  are two points in a plane, then every point of the line  AB  is in the plane, too

    two intersecting straight lines in space lie in a unique plane

   
SAS, ASA, SSS tests for triangle congruence

    SAS, AA, SSS tests for triangle similarity



Know some facts about geometry


    the symmetries of an equilateral triangle

    the symmetries of an isosceles triangle

    know some symmetries of squares and rectangles and cubes

    the formalities of measuring lengths of line segments

    the formalities of measuring the angle between two rays

    two distinct but intersecting lines lie in a unique plane

    any triangle lies in a unique plane

    how to measure the dihedral angle between two intersecting planes

    the intersection of a sphere an a plane is a circle


    the shortest distance between two points on a sphere is along an arc of a great circle


    inclusion-exclusion property for area


    similarity tests for similarity of right triangles

    lines are parallel if and only if they have the same slope in a Cartesian coordinate

   system

    in a Cartesian coordinate system the points which satisfy a linear equation lie on a

   straight line

Calculations

 

    Distance formula for the distance between points in a Cartesian coordinate system

 

    Midpoint formula in Cartesian coordinate system

 

    Slope of a line

    composition (multiplication) of symmetries

    the sum of the measures of the three angles inside a triangle is 180º

    the sum of the measures of the four angles inside a quadrilateral is  360º

    the sum of the measures of the angles inside an n-sided polygon is  180º × (n - 2)

    the measure of each interior angle of a regular   n-sided  polygon

    volume and surface area of spheres, cylinders, prisms, cones, pyramids


    conversions between English and metric units of measurements

   
area and perimeter of rectangles, triangles, trapezoids, parallelograms, circles

   
be able to calculate using the Pythagorean theorem

    use of similar triangles in indirect measurement



Constructions

    use of straight-edge and compass


   
copying  line segments and angles

    constructing the perpendicular bisector of a line segment

    bisecting an angle

    sum, difference of lengths

    use of similar triangles and a unit length to construct products and reciprocals of lengths



Notation

AB  for the line through  points  A  and  B

AB  for the line segment

AB  for the length of the line segment  AB

AB  for the ray with endpoint  A  and passing through  B

     ABC  for the triangle with vertices  A, B, and  C

angle measurement in degrees

for similarity and congruence of triangles