how to use geolegs by thebest11

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									 GeoLeg™                                       Protractor/Compass
                                                Measure and Draw

 Four-In-One geometry tool for
 teachers and students




                         Raise Test Scores
                        Target Geometry and
                           Measurement
                            Grades 4-12




www.geoleg.com                                888-595-5347
                   INVESTIGATING CIRCLES
  USE GEOLEGS OVER WHITE SURFACES OR ON OVERHEAD.


           –– Circle



         –– Blue Sleeve



         –– Red Leg                 Open GeoLeg by rotating red
                                    leg clockwise




                                                                 0




• Discover relationships of angles to circles.
• Draw a circle on grid paper and count number of square grids that form the area.
• Compare the squares counted to the area found with A = πr2.
• Measure the length of the circumference of the circle.
• Compare the area to circumference.
• Draw a square around the circle and count the area out of the circle.
• Find factors of 360º to use for designing circle art.
• Express data through circle graphs.
           FINDING AND MEASURING ANGLES
BLUE LINE IS SET ON 0º AND 180º. RED LINE GIVES ANGLE MEASURE.
                               Intersecting lines form four angles with special
                                                relationships.




                          Vertical angles are congruent,    Supplementary angles are
                              opposite and reflective.     adjacent and have a sum of 180º.
                            60 + 120 + 60 + 120 = 360               60 + 120 = 180

                                    Classify angles
 Obtuse angle/arc                       by their
  90º < B < 180º                      measures.




  Acute angle/arc
    0º < A < 90º                                           Complementary angles
                                                             have a sum of 90º.
                                                              ∠x = 30
                                                              ∠y = 90-30 = 60
                    Straight angle D = 180º
                        Semicircle = 180º
                          Circle = 360º
                                                            Tangent forms a right
                                                              angle to a radius
         Right angle C = 90º
              Arc = 90º




                     Parallel Lines
                   ∠1 = ∠1
                  ∠2 = ∠2
                 ∠1 + ∠2 = 180º
                ∠1 + ∠2 + ∠1 + ∠2 = 360º
                  MEASURE LENGTHS
  USE GEOLEGS OVER WHITE SURFACE OR ON OVERHEAD.


                          Measure from Center
                                       This pencil is 10cm long.




                  10 cm                              7 cm
                                   +
                                       This pencil is 17cm long.


Combine Lengths




                    Total length is 34 cm
                     BUILD POLYGONS BY
                   SLIDING THREE OR MORE
                     GEOLEGS TOGETHER.

                    Round angle measures
                        to nearest 5º.
        Build a Triangle
        1. Turn 3 GeoLegs right side up.
        2. Open GeoLegs by rotating red leg clockwise.
        3. Slide GeoLegs together leg to sleeve.
        4. Choose one length and set it. Hold length in place and choose another.
        5. To increase or decrease an angle measure, increase or decrease the
           length of the opposite side.
        6. Round angle measures to the nearest 5º.
        7. For length of side, add blue seven to red length.
        8. Round lengths to the nearest .5cm.

                                         Isosceles Right Triangle
                                              Round angle               Relationships seen:
                    45º                         measures                Sum of interior angles 90 + 45 + 45 + = 180º
                                              to nearest 5º.            Sum of exterior angles 90 + 135 + 135 = 360º
7cm + 4cm = 11cm




                                    7c




                                                                        Perimeter               11 + 11 + 15.5 = 37.5cm
                                     m
                                         +
                                         8.




                                                                        Longest side opposite largest angle.
                                             5c




                           45º
                                              m




                                                                             (hypotenuse and right angle)
                                                  =
                                                  15




                                                                        Same number of congruent sides and angles (2)
                                                      .5
                                                      cm




                                                                        One line of symmetry. (formed by congruent legs)
                                                                        Pythagorean Theorem            112 + 112 = 15.52
                           90º               45º                             (a + b = c )
                                                                               2   2    2

                     90º                                   45º          90º – 45º – 45º Theorem        15.5 = 11√2
                                                                             (hypotenuse = leg √2)
                            7cm + 4cm = 11cm


                                                                                                   10cm
                           Parallelogram
  Relationships seen:
  Opposite sides are congruent
  Opposite angles are congruent
                                                                                                 60º
                                                                 11cm              120º
  Opposite sides are parallel
  Adjacent angles are
    supplementary
                                                                                                          11cm
  Diagonals bisect each other                                                          120º
  Sum of interior angles                                                  60º
    120 + 60 + 120 + 60 = 360
  Sum of exterior angles
    60 + 120 + 60 + 120 = 360
                                                                        10cm
      USE GEOLEG TO DRAW AND CONSTRUCT
               • USE SHARP OR MECHANICAL PENCILS.
               • WORK ON FLAT SURFACE
               • USE MASKING TAPE IF PAPER SLIPS
                                                                                                      18
                                                                                                        0            15 30 45 60
                                                                                                                                          75




                                                                                             16
                                                                                               5
                                                                                                                                  L




                                                                                     15




                                                                                                                                               90
                                                                                        0




                                                                                                                                               105 120 135 150
                                                                               135 120 105 9




                                                                                                      GEO
                                                                                                                                  EG
                                     hinge




                                                                                             0




                                                                                                                                           16
                                                                                                 75




                                                                                                                                          5
                                                                                                                                      0
                                                                                                        60
                                                                                                                      45 30 15




                                                                                                      3 CM
                                         legs




                                                                                                 4
                                                                                         5




                                                                                                                              4
                                                                                                                          3247
                                                                                                                      : 57
                                                                                   6




                                                                                                                                                                 CM
                                   endpoints




                                                                                                                  TENT




                                                                                                                                                                  7
                                                                                                             US PA
                                                                               7
                                                                           8
                                                                       9
                                                                  10
                        GeoLeg is a better compass




                                                             11
        Old                                                                                                                       New



                                                        12




1. Draw angles using GeoLeg.
   a. Open GeoLeg to desired measure.
   b. Mark vertex and points on each leg.
   c. Connect points.



                                         45º




2. Draw square (or any regular polygon)
                                                        m




                                                                                                                                                             3c
                                                       3c




                                                                                                         90º
                                                                                                                                                                 m




   a. Know interior angle measures (90º).
   b. Open GeoLeg to 90º.
   c. Mark first vertex and 3cm points on each leg.
   d. Connect points.
   e. Measure and mark last 90º angle with 3cm legs.
   f. Connect points to draw a square.
                                     3. Circles can be drawn using GeoLeg center as a pivot
                                        point.
                                        Use drawing points on the leg to draw a circle.
                                        The length of the radius is determined by the drawing
                                        point chosen on the leg.
                                        The radius can be 3cm, 5cm, 7cm, 9cm or 11 cm.
                                        a. Mark the center point of a circle.
                                        b. Place the GeoLeg center over the point.
                                        c. Use a pencil to hold the center as a pivot point.
                                        d. Place a second pencil in the drawing point.
                                        e. Rotate the pencil to draw the circle.
                                        f. Use the straight edge to draw the radius and record
                                           its measure.

4. Trace a circle using GeoLeg as a pattern. GeoLeg has a radius of 2.2cm.
   a. Mark a center point.
   b. Use a pencil or toothpick to hold the center as a pivot point.
   c. Use a pencil to trace a circle around GeoLeg, pushing the legs
      out of the way.


                       5. Concentric circles are two or more circles
                          that have the same center.
                          Draw concentric circles.
                          a. Mark a center point.
                          b. Draw circles with different radii around
                             the center point.



                                                                          180
6. Art Design to try.
   a. Mark a center and draw concentric circles with radii of
      3cm and 5cm.
   b. Mark points on the 5cm circle at 0, 90, 180 and 90.
   c. Connect the opposite points on the circle with          90                        90
      diameters.
   d. Draw squares by connecting 0 to 90, 90 to 180, 180 to
      90 and 90 to 0 in both circles.
   e. Develop a pattern of colors.
                                                                             0
7. Inscribe a hexagon in a circle.                                        180
   a. Mark a center and draw a circle.
   b. Using the GeoLeg circle as a pattern, mark points at
      0, 60, 120, 180, 60, 120.                              120                       60
   c. Write the measures outside the circle.
   d. Connect points (consecutively) 0 to 60, 60 to 120,
      120 to 180, 180 to 60, 60 to 120, 120 to 0.
   e. Draw a triangle:                                        60                       120
      connect points 0 to 120, 120 to 60, 60 to 0
   f. Draw another triangle:
      connect points 60 to 180, 180 to 120, 120 to 60.                       0
             Sample Lesson




Each student needs 4-6 GeoLegs for building polygons.

                 888-595-5347

								
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