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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
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6.1 Basic Geometric figures
Perpendicular Lines
- Two lines a perpendicular if they intersect to form a right angle
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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
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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
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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
- (n-2)*180 degrees
- 2) Sum of three angles in a triangle is 180 degrees
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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
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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= s2
- 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
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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
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- Diamter d = 2*r
- Radius r=d/2
- Circumference - when radius is known
- C=2πr
- Circumference when Diameter is known
- C=πd
- Area
- A=πr2
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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=πr2 h
- 3)Spheres
- V=4/3πr3
- 4)Cones
- V=1/3*B*h or V=1/3πr2 h
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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
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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
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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
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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
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