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