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Module 3 Unit 1 Notes

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					                                           November 30, 2012




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                                                                                                                                                                                                 November 30, 2012

6th Grade Module 3 Unit 1 Day 1 Notes
GEOMETRY Vocabulary:

  Point-­‐	
  	
  an	
  exact	
  loca*on,	
  represented	
  by	
  a	
  ______________ Line-­‐	
  a	
  straight	
  path	
  through	
  __________	
  extending	
  forever	
  in	
  
                                                                                                             opposite	
  direc*ons




  Ray-­‐	
  part	
  of	
  a	
  line,	
  has	
  one	
  _____________	
  and	
  extends	
  in	
  the	
          Line	
  segment-­‐	
  part	
  of	
  a	
  line,	
  with	
  ____________endpoints
              other	
  direc*ons




  Plane-­‐	
  flat	
  surface	
  that	
  has	
  _________	
  thickness,	
  extends	
  forever                  Congruent-­‐	
  figures	
  with	
  ___________shape	
  and	
  size	
  (EQUAL)




  Angle-­‐	
  two	
  _______________with	
  a	
  common	
  endpoint                                         Vertex-­‐	
  the	
  common	
  ________________________




  Right	
  angle-­‐	
  _____________angle                                                                Acute	
  angle-­‐	
  angle	
  measuring	
  greater	
  than	
  ____________	
  and	
  

  	
                                                                                                         less	
  than	
  _____________




  Obtuse	
  angle-­‐	
  angle	
  measuring	
  greater	
  than	
  ________________                             Straight	
  angle-­‐	
  _________________angle

              and	
  less	
  than	
  ______________________




  Complementary	
  angles-­‐	
  the	
  ________of	
  two	
  angles	
  is	
                                  Supplementary	
  angles-­‐	
  the	
  __________of	
  two	
  angles	
  is	
  

              _______________                                                                                   ____________________




Example 1:                                                                                       List:
                                                                                                           three points
                                             K
                                   M                                                                       three lines
                                                          N
                                                                                                           a plane
                                    J                   L
                                                                                                           three rays

                                                                                                           three line segments



Example 2:                                                                                               Find the measure of each angle and describe the
                                             R                                                           angle type.
                                                                                                               a) PQR
                                                                 S
                                                                                                                 b) RQS
                                            60o
            P                   90o                       30o
                       30o                                                                                       c) UQR
                                          Q                            T
                                                                                                                 d) PQT
                     U


         Use the figure to complete the statements.

                    a) ≮RQS and ≮SQT are ________________________________angles


                    b) ≮PQS and ≮SQT are ________________________________angles
                                                  November 30, 2012




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PROBLEM OF THE WEEK!
                                                                                                                                                                                             November 30, 2012

Line and Angle Relationships Notes
Geometry	
  Vocabulary:

Perpendicular	
  lines-­‐	
  lines	
  that	
  intersect	
  at	
  _______________angles                Parallel	
  lines-­‐	
  lines	
  in	
  the	
  same	
  plane	
  that	
  do	
  not	
  
                                                                                               __________________




Skew	
  lines-­‐	
  lines	
  that	
  do	
  not	
  intersect	
  and	
  are	
  not	
  ________________      Adjacent	
  angles-­‐	
  two	
  angles	
  that	
  share	
  a	
  
          (they	
  are	
  in	
  different	
  planes!)                                                 ______________and	
  _________________,	
  but	
  no	
  
                                                                                                  common	
  interior	
  points




VerFcal	
  angles-­‐	
  ____________________angles	
  formed	
  when	
  two	
  lines         Transversal-­‐	
  a	
  line	
  that	
  ___________________two	
  or	
  
      intersect.                                                                  more	
  lines	
  that	
  lie	
  on	
  the	
  same	
  plane




Corresponding	
  angles-­‐	
  angles	
  in	
  corresponding	
  ____________________   Interior	
  angles-­‐	
  angles	
  __________________	
  the	
  two	
  
       (In	
  the	
  same	
  posi*on	
  in	
  rela*on	
  to	
  the	
  transversal)  parallel	
  lines	
  (with	
  transversal)




Alternate	
  interior	
  angles-­‐	
  interior	
  angles	
  on	
  ____________________	
  sides	
   Exterior	
  angles-­‐	
  angles	
  ___________________the	
  
        of	
  the	
  transversal                                                           parallel	
  lines	
  (with	
  transversal)




Alternate	
  exterior	
  angles-­‐	
  exterior	
  angles	
  on	
  _____________________
       Sides	
  of	
  the	
  transversal




 Example 1: Identifying Adjacent Angles
 a)  Name all pairs of adjacent, supplementary angles.
                                                                                                                                                1
                                                                                                                                       4                  2
                                                                                                                                                 3
 b)        Name the vertical angles.




                                                                                              Example 2: Using Vertical Angles
                                                                                              a) Given that m≮1 = 75o, find m≮3.
                                       1
                                               2
                                     4       3                                                b) Find the m≮2.



                                                                                              c) Find the m≮4.


                                                                                              d) Name 2 adjacent, supplementary angles.
                                                    November 30, 2012




         Welcome to Class!

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Put your homework on the top left corner of your desk

PROBLEM OF THE WEEK!
                                                                                    November 30, 2012




Review Line and Angle Relationships Notes


Example 1: Identifying Parallel, Perpendicular, and Skew Lines
    Tell whether the lines in the figure appear parallel, perpendicular, or skew.


a)     AB and AC



b)     CG and BD



c)     AC and BD




 Example 2: Using Angle Relationships to Find Angle Measures
     Line n ll p. Find the measure of each angle.



  ≮1                     ≮4

  ≮2                     ≮5

  ≮3                     ≮6
                                                        November 30, 2012




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PROBLEM OF THE WEEK!
                                                                                                         November 30, 2012

Classifying Polygons Notes
 Geometry Vocabulary:


 Polygon- a simple, closed plane figure formed by      Regular polygon- polygon with all sides and all
 ___________ or more line segments                     angles ____________

Examples:                     Non-Examples:




Example 1:
    Determine whether each figure is a polygon. It if is not, explain why not.




 Example 2:
     Name each polygon.




  Example 3:
      Name each polygon and tell whether it is a regular polygon. If it is not, explain why not.
                                                    November 30, 2012




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                                                                                 November 30, 2012




 Classifying Triangles Notes




Example 1: Classify each triangle by its sides and then by its angle measures.




  Example 2:
      Identify the different types of triangles in the figure, and determine how many of
      each there are.
                                           November 30, 2012




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                                                                                                    November 30, 2012

Classifying Quadrilaterals Notes
  Geometry Vocabulary:

 Parallelogram- quadrilateral with opposite sides
       _____________and _______________.
       (Opposite angles are ≅)



                                             Rectangle- parallelogram with ______________right
                                                  angles and ______________________ sides
                                                  are congruent.




  Rhombus- parallelogram with
      _____________congruent sides.




                                             Square- parallelogram with ______________congruent
                                                  sides and four _________________angles.




 Trapezoid- exactly one pair of opposite sides is
      ______________



 Example 1:
      Give all of the names that apply to each quadrilateral. Then give the name that best
 describes it.




 Example 2:
     Draw each figure. If it is not possible to draw, explain why.

 a)   A rectangle that is not a square.             b)   A rectangle that is not a parallelogram.
                                                        November 30, 2012




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                                                                                                         November 30, 2012
Interior Angle Sums of Triangles and Quadrilaterals Notes


  The sum of the angles in a triangle equal 180˚




Find the unknown angle measure in the triangle.

 Example 1:                                         Example 2:




  Example 3:
      A right triangle with one angle measure of 36o




                                                   The sum of the angles in a quadrilateral equal 360˚




     Find the unknown angle measure in the quadrilateral.


 Example 4:                                        Example 5:




  Example 6:
      A quadrilateral with angle measures of 144o, 84o, and 48o
                                                        November 30, 2012




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PROBLEM OF THE WEEK!
                                                                                                November 30, 2012

Interior Angles of Polygons Notes

  Triangle- interior angles equal _____________________

  Quadrilateral- interior angles equal ________________________

  All polygons- divide it into triangles, multiply ______________________ by the number of
        triangles


Example 1:
    Divide the polygon into triangles to find the sum of its angle measures.




 Example 2:
     Find the sum of the interior angles of each polygon.




 Example 3:




                   Number of Number of
      Figure
                     Sides   Triangles

  Quadrilateral         4

  Pentagon              5

  Hexagon               6

           **The number of triangles is always 2 less than the number of sides of the figure.


Example 4: Find the sum of the interior angles.
November 30, 2012
                                                        November 30, 2012




                Welcome to Class!
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PROBLEM OF THE WEEK!
                                                                                                     November 30, 2012
Similar and Congruent Figures Notes
     Similar figures- figures with the same ______________________, but not the same size

     Congruent figures- similar figures that have the same ____________ AND the same __________­­_

     Corresponding angles- angles that are in the same

      _______________________ in the shape

     Corresponding sides- sides that are in the same

     _______________________ in the shape




Identify the corresponding sides in the pair of triangles. Then use ratios to determine whether
the triangles are similar.




Example 1:
Are these figures similar?

a)                                                        b)




 Example 2:
 Find the unknown measure in the similar figures.

     a)                                                 b)




      Example 3:
      Determine whether the figures are congruent.




          Example 4:
          Determine the unknown measure in each set of congruent polygons.
                                                    November 30, 2012




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ISTEP Packet

PROBLEM OF THE WEEK!
                                                                                               November 30, 2012

Transformations and Symmetry Notes
     Transformations- changing the ______________________of a geometric figure

                         Types of Transformations
     Translation- __________________             Reflection- ___________________




     Rotation- __________________




Example 1:
    Name the transformation in each figure.




Example 2:
    Decide whether each of the figures has line symmetry. If it does, draw all the lines of
    symmetry.




Line Symmetry- drawing a line down the _____________________of a figure, producing the exact
same image on both sides of the line
Rotational Symmetry- figure is rotated less than 360o and it is the original shape


Example 3:
    Tell how many times each figure will show rotational symmetry within one full rotation.
                                           November 30, 2012




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Review for your homework quiz

PROBLEM OF THE WEEK!
                                           November 30, 2012




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PROBLEM OF THE WEEK!

GOOD LUCK
November 30, 2012

				
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