2. Geometry (HS)

 
  1. Reasoning About Numbers, Systems and Quantitative Situations (L1)
  2. Calculation, Algorithms, and Estimation (L2)
  3. Mathematical Reasoning, Logic, and Proof (L3)
  4. Figures and Their Properties (G1)
  5. Relationships Between Figures (G2)
  6. Transformations of Figures in the Plane (G3)

 

Additional Links to General Mathematics Sites

 

5. Figures and Their Properties (G1)

Students represent basic geometric figures, polygons, and conic sections and apply their definitions and properties in solving problems and justifying arguments, including constructions and representations in the coordinate plane. Students represent three-dimensional figures, understand the concepts of volume and surface area, and use them to solve problems. They know and apply properties of common three-dimensional figures.

 

High School

  1. G1.1 Lines and Angles; Basic Euclidean and Coordinate Geometry
    1. Angles and Parallel LinesThis site has an interactive applet that allows geometry students to discover properties of parallel lines. Access the applet by clicking on "11-14" at the left side of the webpage. Locate "Angles and Parallel Lines" from the drop down menu to use the applet.
    2. BGfl New
      Very visual site for 3D items. Shows rotations, has nets that can be printed out for shapes, and gives important related terms.
    3. Exterior Angles Conjectures
      Student interactive site which allows the student to see a demonstration of the exterior angles conjecture.
    4. Formulas From Geometry. Good Visuals New
      This is a video of a self tutorial about algebraic formulas from geometry
    5. Geometry: From the Land of the Incas
      Students will find an eclectic mix of sound, science, and Incan history in order to raise interest in Euclidean geometry. Geometry problems, proofs, quizzes, puzzles, quotations and visual displays are included. The site also has a section on Geometry Theorems and Problems and quizzes in other areas mathematics.
    6. Guessing Correlations
      This is an interactive site for students.  They are asked to look at a linear regression graph and decide an approximate value for the correlation coefficient.
    7. Math League New
      Includes a list of basic terms for lines and segments, good descriptions and also provides examples.
    8. Rectangle Conjectures
      An activity that always students to discover the properties of rectangles.  It provides a method to discover the properties using pencil and paper or geometer sketchpad.
    9. The Moving Sofa Problem
      Students must determine whether couches, of varying shapes, can fit around a narrow corner. In addition, students calculate areas of different shaped furniture and explore properties of regular and irregular objects.
    10. Water to the Max
      This is a teacher lesson plan of a student activity.  It includes measuring angles and the distance of water flowing through a garden hose at the different angles.  This lesson is one which can be done in class, however it will work equally as homework or extra credit assignment. It was designed  by a teacher/ track coach and this activity could be used to help athletes see what they should do to maximize their performance. This activity is a great deal of fun in the spring of the year when the students want to get outside to enjoy the great outdoors and the water.
  2. G1.2 Triangles and Their Properties
    1. Impossible Triangles
      Given properties of triangles, students will determine why it is impossible to create a triangle with the given dimensions. Students can enter answers and check them as they go.
    2. Isosceles Trapezoid
      An activity that always students to discover the properties of an isosceles trapezoid.  It provides a method to discover the properties using pencil and paper or geometer sketchpad.
    3. Pythagorean Puzzle
      Outstanding - This site gives a proof of the pythagorean theorem using squares that students can move around. It provides a useful link to real-life Pythagorean applications under puzzles.
    4. The Geometers Sketchpad (Three Labs) 
      Students use Geometer's Sketchpad to investigate properties of parallelograms, rectangles, and triangles. Requires the program Geometer's Sketchpad.
    5. The Pythagorean Theorem: Figure It Out All By Yourself
      This site provides a guided interactive discovery of the Pythagorean Theorem with the ability of students to record and compare their results. Included is a brief history of Pythagoras and additional applications of the Pythagorean Theorem.
  3. G1.3 Triangles and Trigonometry
    1. Dave's Short Trig Course
      This site contains a thorough tutorial on the concepts of trigonometry and application of trig functions.  It could be used by both teachers and students.  There are clear explanations and pictures as well as student practice problems.  Also included are application to the real world.  If  there is anything a students needs to know associated with a trigonometry lesson, it can surely be found here.
    2. Geometry: Special Triangles
      This site provides an explanation of various properties of special right triangles.  Then it gives a few examples for the students to try.  It also provides a quiz for the students to take.
  4. G1.4 Quadrilaterals and Their Properties
    1. Quadrilateral Sum Conjecture
      Student interactive site which allows the student to see a demonstration of the quadrilateral sum conjecture.
  5. G1.5 Other Polygons and Their Properties
    1. Congruent Figures New
      This information can function as both a student interactive and teacher resource. It presents Congruent figures using a four step approach. Step 1 is First glance, Step 2 is In depth, Step 3 is Examples, and Step 4 is work out.
    2. Math League New
      This site gives several polygons and some of their characteristics including the interior angle sum. This is good to use in comparing several different polygons at once.
    3. Parallelogram Conjectures
      An activity that always students to discover the properties of a parallelogram.  It provides a method to discover the properties using pencil and paper or geometer sketchpad.
    4. Polygon Sum Conjecture
      Student interactive site which allows the student to see a demonstration of the polygon sum conjecture.
    5. Reflect on This
      This site, by NCTM (Illuminations) provides a lesson on symmetry for high school geometry students. In this lesson, the student will build a kaleidoscope and use reflection to create and measure polygons. Reproducible activity masters can be downloaded by the teacher.
    6. Studying Polyhedra
      Students take a look at several rotating polyhedra. Students can count the number of faces, edges, and vertices. There are many links to other sites that can add more depth to understanding polyhedras.
  6. G1.6 Circles and Their Properties
    1. Designs With Circles
      A circle construction activity that explores reflectional and rotational symmetry.
    2. Ellipse Game 
      You will be given an ellipse of random dimensions and you will have to try to click on one of the foci. Should you fail in this mission at first, you will be given some clues. Helps student get a feel for where the foci of a ellipse are located.
    3. Properties of Circles
      Students measure circular objects to discover the ratio of the circumference of a circle to it's radius of a circle. This site is not student interactive but contains printable student worksheets and teacher reference materials.
    4. Regents Exam Prep Center New
      Good examples of cirlces and their characteristics. Offers practice problems and teacher suggestions for activities.
    5. Shaded in Four Circles
      Four congruent circles each tangent to two of the other. The centers are connected to form a square. Find the estimated area formed between the circles. This is not an interactive site.
  7. G1.8 Three-Dimensional Figures
    1. Math.com -Three dimensional figures
      This site takes you through a four step process in helping you solve multistep problems involving volumes of cylinders, spheres and cones. Students get to do work out problems on step 4.

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