Review Sheet 3 Math 106

New material after midterm 2 is in** bold itali**

**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

**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
*

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*