Geometry Review

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Author:
treborprime
ID:
25558
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Geometry Review
Updated:
2010-07-02 18:11:07
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WGU Geometry review
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QLC1 Geometry review
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  1. 6.1 Basic Geometric figures
    1) Segment
    2) Ray
    3) Line
    • 1) A segment is a geometric figure consisting of two points called endpoints.
    • 2) Ray Consists of a segment and all points between A and B and all points beyond b
    • 3) Line Can consist of two rayes such as PQ and QP - can be named as a smaller letter m
    • Lines can be coplanar - Parrallel (l||m) or they can be intersecting
  2. 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
  3. 6.1 Basic Geometric figures
    Perpendicular Lines
    • Two lines a perpendicular if they intersect to form a right angle
  4. 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
  5. 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. 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
  7. 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
  8. 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
  9. 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=πr2
  10. 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
  11. 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
  12. 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
  13. 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
  14. 6.6 Relationships between Angle measures - Transversals and Angles
    1) Define a transversal
    2) what are the angle types formed?
    • 1) A transversal is a line that intersects two or more coplanar lines in different points
    • When a transversal intersects a pair of lines, eight angles are formed
    • 2) - Angle types formed
    • Corresponding Angles - expressed in pairs
    • <2 and <6, <3 and <7, <1 and <5, <4 and <8
    • Interior angles - not expressed in pairs
    • <3, <4,<5,<6
    • Alternate Interior Angles - expressed as pairs
    • <4 and <6, <3 and <5
  15. 6.6 Relationships between Angle measures
    Properties of Parralle Lines
    • 1) In a transversal intersects two parallel lines, then the corresponding angles are congruent
    • 2) If a transversal intesects two parallel lines, then the alternate interior angles are congruent
    • 3) In a plane, if two lines are parallel to a third line, then the two lines are parallel to each other

    • 4) if a tranversal intersects two parralel lines, then the interior angles on the same side
    • of the transversal are supplementary
    • 5) if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
  16. 6.7 Congruent triangles and properties of parallelograms
    1) Define Triangle types
    2) Define the three properties to show why triangles are congruent
    • 1) Classify triangles by their angles
    • Acute: All angles are acute ( less than 90 degrees)
    • Right: One angle is a right angle ( 90 degrees)
    • Obtuse: One obtuse angle ( greater than 90 degress less than 180 degrees
    • Equiangular: all angles are congruent
    • 2) Classify triangles by their sides
    • Equilateral: All sides are congruent
    • Isosceles - at least two sides are congruent
    • Scalane - No sides are congruent

    • 3) Three properties to show why triangles are congruent
    • Triangles are congruent if and only if their vertices can be matched so that the corresponding angles and sides are congruent
    • Corresponding sides and angles of two congruent triangles are called corresponding parts of congruent triangles
    • Corresponding parts of congruent triangles are always congruent
    • We write to say that are congruent
    • The side-Angle-Side SAS property
    • Two triangles are congruent if two sides and the included angle of one triangle are congruent to
    • two sides and the included angle of the other triangle

    • The Side-Side-Side (SSS) property
    • If three sides of one triangle are congruent to three sides of another triangle
    • then the triangles are congruent

    • The Angle-Side-Angle (ASA) property
    • If two angles and the included side of a triangle are congruent to two angles and the
    • included side of another triangle , then the triangles are congruent
  17. 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
  18. 6.8 Similar Triangles
    Review similar triangles
    • Triangles can be similar to each other but not congruent in size
    • Two triangles are similar in and only if their vertices can be matched so that their corresponding angles are congruent and the
    • lengths of corresponding sides are proportional
    • To say that <>ABC and <>DEF are similar we write"<>ABC ~<>DEF"
    • Thus, <>ABC ~ <>DEF means that

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