##
Archive for **January 2010**

### Geometry Words

Posted January 28, 2010

on:**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 http://www.thefreedictionary.com/rotation – 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.

Image taken from http://mathworld.wolfram.com/Rotation.html

**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 http://www.thefreedictionary.com/translation – The changing of the coordinates of points to coordinates that are referred to new axes that are parallel to the old axes.

Image taken from http://mathworld.wolfram.com/Translation.html

**3. Tangram**

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

Definition from http://www.thefreedictionary.com/ms – A Chinese puzzle consisting of a square cut into five triangles, a square, and a rhomboid, to be reassembled into different figures

Images taken from http://mathworld.wolfram.com/Tangram.html

**4. Concave**

Personal Definition – a shape that has smooth outward edges

Definition from http://mathworld.wolfram.com/Concave.html– Curved like the inner surface of a sphere.

**5. Convex**

Personal Definition – a shape that has dips or indents

Definition from http://www.thefreedictionary.com/convex – Having a surface or boundary that curves or bulges outward, as the exterior of a sphere

Images taken from http://mathworld.wolfram.com/Concave.html

**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 http://www.thefreedictionary.com/ms – having similarity in size, shape, and relative position of corresponding parts

A B

A image taken from http://www.fotosearch.com/BDX238/bxp41131/

B image taken from http://gwydir.demon.co.uk/jo/symmetry/exsymm.htm

**7. Nonsymmetrical**

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

Definition from http://www.mathresources.com/products/mathresource/maa/nonsymmetric.html – (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 http://www.mathopenref.com/polygonregular.html – A polygon that has all sides equal **and** all interior angles equal (This site has a great interactive object to demonstrate.)

A A B

A images from http://planetmath.org/encyclopedia/RegularPolygon.html

B image from http://geography.about.com/library/photos/blzz73.htm

**9. Equilateral Triangle**

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

Definition from http://en.wikipedia.org/wiki/Triangle – In an **equilateral triangle**, all sides have the same length. An equilateral triangle is also a regular polygon with all angles measuring 60°.

Image from http://mathworld.wolfram.com/EquilateralTriangle.html

**10. Obtuse triangle**

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

Definition from http://mathworld.wolfram.com/ObtuseTriangle.html – 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.)

Image from http://mathworld.wolfram.com/ObtuseTriangle.html

**11. Quadrilateral**

Personal definition – a four sided polygon

Definition from http://mathworld.wolfram.com/Quadrilateral.html – 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.

Images from http://mathworld.wolfram.com/Quadrilateral.html

**12. Trapezoid**

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

Definition from http://www.mathopenref.com/trapezoid.html – 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.

Image from http://id.mind.net/~zona/mmts/geometrySection/commonShapes/trapezoid/trapezoid.html

**13. Parallelogram**

Personal Definition – a quadrilateral with opposite sides parallel and congruent

Definition from http://www.ies.co.jp/math/products/geo1/applets/para/para.html – A parallelogram is a quadrilateral that has two pairs of parallel sides.

A B

A image from http://www.ies.co.jp/math/products/geo1/applets/para/para.html

B image from http://www.usefilm.com/image/1107115.html

**14. Rhombus**

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

Definition from http://www.mathopenref.com/rhombus.html – *A quadrilateral with all four sides equal in length.*

B image from http://en.wikipedia.org/wiki/Rhombus

**15. Square**

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

Definition from http://mathworld.wolfram.com/Square.html – a geometric figure consisting of a convex quadrilateral with sides of equal length that are positioned at right angles to each other

Image from http://mathworld.wolfram.com/Square.html

B image from http://media.photobucket.com/image/squares/caroljt/IMG_2113.jpg?=24

**16. Pythagorean Theorem**

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

Definition from http://mathworld.wolfram.com/PythagoreanTheorem.html – For a right triangle with legs and and hypotenuse ,

Image taken from http://mathworld.wolfram.com/PythagoreanTheorem.html

**17. Dilations**

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

Definition from http://mathworld.wolfram.com/Dilation.html – 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.

Image taken from http://mathworld.wolfram.com/Dilation.html

### Hello Everyone

Posted January 27, 2010

on: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

Roberta