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.
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    • 2) Ray Consists of a segment and all points between A and B and all points beyond b
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    • 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
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  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
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    • 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
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  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
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  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)
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    • 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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  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
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    • 3)Spheres
    • V=4/3πr3
    • 4)Cones
    • V=1/3*B*h or V=1/3πr2 h
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  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
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    • 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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  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
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    • 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
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    • <2 and <6, <3 and <7, <1 and <5, <4 and <8
    • Interior angles - not expressed in pairs
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    • <3, <4,<5,<6
    • Alternate Interior Angles - expressed as pairs
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    • <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
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    • 2) If a transversal intesects two parallel lines, then the alternate interior angles are congruent
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    • 3) In a plane, if two lines are parallel to a third line, then the two lines are parallel to each other
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    • 4) if a tranversal intersects two parralel lines, then the interior angles on the same side
    • of the transversal are supplementary
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    • 5) if a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other
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  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 Image Upload to say that Image Upload are congruent
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    • 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
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    • 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"
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    • Thus, <>ABC ~ <>DEF means that
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Author:
treborprime
ID:
25558
Card Set:
Geometry Review
Updated:
2010-07-02 22:11:07
Tags:
WGU Geometry review
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Description:
QLC1 Geometry review
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