Roberta's Blog

Archive for January 2010

1. Rotation

 Personal Definition – the object is moving around.  When teaching to students it is important that they understand that there is a set point in which the object is moving around. The point can be anywhere in/or the object or somewhere outside the object.

Definition from – A transformation of a coordinate system in which the new axes have a specified angular displacement from their original position while the origin remains fixed.


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2. Translation

Personal Definition – slide an object with any rotation or flipping. When teaching students it is important they understand that the orientation of the object remains the same just the position of the object changes

Definition from – The changing of the coordinates of points to coordinates that are referred to new axes that are parallel to the old axes.


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3. Tangram

Personal Definition – seven puzzle pieces that are very specific in size and shape and when put together create a square.

Definition from –   A Chinese puzzle consisting of a square cut into five triangles, a square, and a rhomboid, to be reassembled into different figures


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4. Concave

Personal Definition – a shape that has smooth outward edges

Definition from– Curved like the inner surface of a sphere.

5. Convex

Personal Definition – a shape that has dips or indents

Definition from – Having a surface or boundary that curves or bulges outward, as the exterior of a sphere


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6. Symmetrical

Personal Definition – a shape that can be divided in half and both halves match exactly. It can be divided vetically or horizontally.

Definition from –   having similarity in size, shape, and relative position of corresponding parts

AClipart - butterfly fantasy.  fotosearch - search  clipart, illustration,  drawings and vector  eps graphics images     B

A image taken from 

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7. Nonsymmetrical

Personal Definition – a shape that cannot be divided so that each side matches the opposite side.

Definition from –   (of a figure or configuration) not identical with its own reflection in an axis of symmetry or center of symmetry

8. Regular Polygon

Personal Definition – a polygon in which all the sides and angles are congruent

Definition from – A polygon that has all sides equal and all interior angles equal (This site has a great interactive object to demonstrate.)

 A     $\textstyle \parbox{5.84958pc}{\begin{center}\begin{xy} 0;<3pc,0pc>:<0pc,3pc>:: ... ... \ar@{-}c+(0.193096,1.52446);c+(0.974928,1.90097) \end{xy}heptagon\end{center}}$  A  $\textstyle \parbox{5.70633pc}{\begin{center}\begin{xy} 0;<3pc,0pc>:<0pc,3pc>:: ... ...11803) \ar@{-}c+(0.,1.11803);c+(0.951057,1.80902) \end{xy}pentagon\end{center}}$Photograph of a Stop Sign

A images from

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9. Equilateral Triangle

Personal Definition – three sided polygon that has congruent sides and angles

Definition from –  In an equilateral triangle, all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.


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10. Obtuse triangle

Personal definition – a triangle with one angle greater than 90°

Definition from – An obtuse triangle is a triangle in which one of the angles is an obtuse angle. (Obviously, only a single angle in a triangle can be obtuse or it wouldn’t be a triangle.)


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11. Quadrilateral

Personal definition – a four sided polygon

Definition from – A quadrilateral, sometimes also known as a tetragon or quadrangle (Johnson 1929, p. 61) is a four-sided polygon. If not explicitly stated, all four polygon vertices are generally taken to lie in a plane.


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12.  Trapezoid

Personal Definition – a four sided polygon (quadrilateral) with one side of parallel sides

Definition from – A quadrilateral which has at least one pair of parallel sides. Every trapezoid has two bases, these are the parallel sides. The non-parallel sides are legs. Every trapezoid has two legs.

The Trapezoid

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13. Parallelogram

Personal Definition – a quadrilateral with opposite sides parallel and congruent

Definition from – A parallelogram is a quadrilateral that has two pairs of parallel sides.

A    B Parallelogram

A image from

B image from

14. Rhombus

Personal Definition – a four sides object with opposite sides are parallel and all sides are congruent

Definition from  – A quadrilateral with all four sides equal in length.

  B  File:Rhombus.svg

A image from

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15. Square

Personal Definition – four sided polygon with congruent sides, opposite sides parallel, and four right angles.

Definition from –  a geometric figure consisting of a convex quadrilateral with sides of equal length that are positioned at right angles to each other

A Square  B IMG_2113.jpg 3/4 Inch Squares image by caroljt 

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B image from

16. Pythagorean Theorem

Personal Definition – When the squares of the two legs of a right triangle equal the square of the hypthenuse.

Definition from  –  For a right triangle with legs a and b and hypotenuse c,  a^2+b^2=c^2.


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17. Dilations

Personal Definition – When a shpae is enlarged or shrunk using a mulitplier

Definition from – A similarity transformation which transforms each line to a parallel line whose length is a fixed multiple of the length of the original line. The simplest dilation is therefore a translation, and any dilation that is not merely a translation is called a central dilation. Two triangles related by a central dilation are said to be perspective triangles because the lines joining corresponding vertices concur. A dilation corresponds to an expansion plus a translation.


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I want to tell you a little about myself. I come from a large family. I have 3 brothers and 3 sisters. All of us still live in Illinois so I am still able to see them a few times a year.

I have been married for over 25 years to the same person, he is my backbone. We have two wonderful grown sons who both live about 30 miles away. I finally got a daughter two years ago when my oldest son got married. Grandchildren are not a part of our lives right now but I am sure they will be in the upcoming years.

I teach in the same school district that I graduated from, it was one of my goals as a teenager. The name of the district where I teach is PORTA CUSD #202 in Petersburg, IL. It is a unit district in a rural farming community.

I am taking this course so that I can stay on top of what is going on in the geometry classroom and to help the teachers I work with stay attune to what is going on. Two things I would like to get out of this class are ways to help my fellow teachers strengthen the geometric abilities of their students and to find activities that those teachers can implement to involve transformations into their teaching.

Have a Great Day




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  • Judy: Roberta, The Transformational Golf is a new site for me. I haven't seen this one and can't wait to share it with others. Many students struggle w
  • bkgeary: I like the idea of letting the student pick the material. Students never fail to amaze me with the great ideas that they come up with. I think that
  • joshbeals: I love puzzles too! I liked your comments about quilting patterns. It's awesome when we see math in the things we choose to do with our free time.