

6.1 Basic Geometric Figures Angles
1) What is an Angle
2) Types of Angles
 1) An Angle is a set of points consisting of two rays or half lines with a common end point, this end point is called a vertex
 Unit of Measure is degrees
 2) Types of Angles
 a) Right angle = 90 degrees
 b)Acute angle  greater than 0 and less than 90 degrees
 c)Obtuse Angle  greater than 90 and less than 180 degrees
 d) Straight angle  measure is 180 degrees

6.1 Basic Geometric figures
Perpendicular Lines
 Two lines a perpendicular if they intersect to form a right angle

6.1 basic Geometric figures  Polygons
What are polygons?
What are the most common polygons?
 1) Polygons are shapes made up of 3 or more sides

6.1 Basic Geometric shapes  Triangles
What is a triangle and what are the different types?
 1) Triangles are polygons of 3 or more sides
 2) types of triangles
 a)Equilateral Triangle  all sides same length
 b)Isosceles Triangle  two sides are the same length
 c)Scalane Triangle  All sides are of different lengths
 d) right triangle  one angle is 90 degrees
 e)Obtuse triangle  One angle is an obstuse angle between 90 and 180 degrees
 f)Acute triangle  all three angles are acute  less than 90 degrees

6.1 Basic Geometric figures  sum of angle measures for polygons
1)How do you find the sum of angles for more complex polygons?
2) What is the sum of angles for all triangles?
 1)Take the number of sides (n) subtract 2 and multiply by 180 degrees
 (n2)*180 degrees
 2) Sum of three angles in a triangle is 180 degrees

6.2 Perimeter og a polygon
1) What is perimeter?
2) Formulas for perimeter of a square and rectangle?
 1) A polygons is a geometric figure with three or more sides.
 The perimeter of a polygon is the distance around it or the sum of length of its sides
 2) Perimeter of a rectangle
 P=2(l*w)
 3) Square
 P=4*s

6.3 Area of Rectangles, Squares, parallelogram, triangle and trapezoid
1) Define area
2) Formulas for areas of various polygons
 1) Area is defined as the measure of the interior form of a plane region
 Area is expressed as squared  IE 5 sqr feet etc
 Square units
 2) Common formulas
 Rectangle  A=l.w
 Square  A= s^{2}
 Parellelogram  A = b*h (four sided figure with two pairs of parallel sides)
 Triangle A= 1/2*b*h
 Trapezoid A=1/2*h*(a+b) (polygon with 4 fours, two of which are bases which are parallel to each other

6.4 Circles  Radius, Diameter, Circumference and Area
1) Define each of Radius, Diameter and Circumference
2) Formulas for each Radius, Diameter and Circumference
 1) Diameter  length across the circle
 Radius  length from center point to end
 Circumference  distance around the circle
 2)
 Diamter d = 2*r
 Radius r=d/2
 Circumference  when radius is known
 C=2πr
 Circumference when Diameter is known
 C=πd
 Area
 A=πr^{2 }

6.5 Volume and Surface Area
1) Define formulas for Rectangule solid, circular cylinder, sphere and cone
 Volume is expressed as cubic units
 1) Rectangular Solids  Volcume is the number of unit cubes needed to fill it
 V=l*w*h
 Surface area of a rectangular solid  total area of the six rectangles that form the surface of the solid
 SA=2(lw+lh+wh)
 2) Cylinders
 V=B*h or V=πr^{2} h
 3)Spheres
 V=4/3πr^{3}
 4)Cones
 V=1/3*B*h or V=1/3πr^{2} h
 ^{}

6.6 Relationships between Angle measures
1)Define complementary and supplementary angles
 1)Two angles are complementary when the sum of their measures is 90 degres
 Each angle is said to complement of the other
 These are said to be acute angles  when they are adjacent they form a right angle
 2) Supplementary angles  angles are supplementary when the sum of the measure is 180 degrees
 Each angle is called the supplement of the other

6.6 Relationships between Angle measures  Congruency
1) define congruent angles and segments
 1) Congruent segments  two segments that have the same length
 2) Congruent angles  angles that have the same measure

6.6 Relationships between Angle measures Vertical Angles
1) define what a vertical angle is
2)What is the vertical angle property?
 1) two nonstraight angles are vertical angles if and only if their sides form two pairs of opposite rays
 Angles RPQ and SPT are called veritcal angles
 2) The vertical angle property  these angles are congruent




6.7 Congruent triangles and properties of parallelograms
Define the properties of parallelograms
 1) A diagonal of a parallelogram determines two congruent triangles
 2) The opposite angles of a paralleogram are congruent
 3) The opposite sides of a paralleogram are congruent
 4) Consecutive angles of a parallelogram are suppelmentary
 5) Diagonals of a parallelogram bisect each other


