Review Sheet 2   Math 106

New material is in italic.  While the emphasis in Midterm 2 will be new material,  previous material may be incorporated.

Know the meaning of

    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



Calculations

    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