# Web Links for Geometry, 4th ed.

## General

*NCTM Student Exploration in Mathematics*—At this site there are a multitude of mathematical explorations for students to work through. The sheets may be downloaded and printed for educational use for members of NCTM. (See copyright information on this site for proper use of the material.)- Math Archives—Gives an index of Math Topics from A to Z
- National Library of Virtual Manipulatives—A great source for electronic manipulatives categorized by subject area and grade level, includes Platonic Solids, transformational geometry and much more
- Download Graph Paper
- Math Forum—Many resources for anyone teaching or learning mathematics
- Ask Dr. Math—Stuck on a problem? Look here for help
- Problems of the Week—From Math Forum
- Project
*Mathematics!*—Several low cost, professional videos are available here on various aspects of mathematics - Mathematical Quotations—Collection of many quotations about mathematics
- World of Math—Helps in all areas of math for the teacher and student
- Math Enrichment Ideas—General math ideas where you can find ideas to bring your class to life
- Biblical Worldview of Mathematics—Very good article written by Georgia Miller clearly articulating the Biblical worldview we should articulate to our students
- Math from a Biblical Worldview—Take a look at the videos at this site

## Geometry Helps

- Euclid’s Elements—English edition of the famous work by Euclid who compiled all geometry of antiquity
- Teaching Geometry According to the Common Core Standards—Written by the author of the geometry section of the CCSS gives more detail as to the reasoning behind the topics included in the standards
- Geometry through Art—Gives ideas to integrate geometry and art
- Teaching Geometry with Google Sketchup—This tool can be fascinating to students and teacher alike, also includes a problem of the month
- Math Bits Geometry Resources—Includes student and teacher resources
- Geometry Labs—Online activities for hands-on activities for a variety of geometry topics
- Teaching Channel—Access to a variety of teaching ideas and videos
- Wolfram Mathematica—Advance mathematical software and reference program
- Geometry using Paper Folding—Many geometric concepts can be developed by simple paper folds

## General Video and Applet Sources

- Science of NHL Hockey: Hockey Geometry—A great video to review basic geometric terms
- pbslearningmedia.org— You can find a variety of geometry videos to choose from at this site, you can set up a free account
- Polygon Dissection Gallery—An excellent video source that can be used in the classroom for many different topics related to polygons from dissection to proofs
- Visual Geometry Pages—Applet for all types of three-dimension figures
- Geometry Java Applet Gallery—A great number of useful applets that can be used to illustrate geometry concepts

## Chapter 1: Foundations of Geometry

### 1.5 Measuring Segments and Angles

- Illuminations: Perpendicular Lines—Perpendicular lines applet
- Illuminations: Soccer Problem—applet that explores the changing angles to the goal as a player moves

### 1.4 Subsets of Lines and Plane

- Illuminations: Line, Ray, Segments—Exploration via applet of these basic figures of geometry

### 1.7 Two-Dimensional Figures

- Illuminations: Geometry of Circles—Review of the relationships between radius, diameter, circumference and area of a circle using a MIRA
- Illuminations: What’s Important about Triangles?—Helps students understand when a triangle can be formed based on side lengths and develops the idea of perimeter of a triangle
- Practice Brownie Perimeters—Find the maximum area with a fixed perimeter using brownies
- Explore Circumference with your Bicycle Wheel—Use a real-world object to discover the meaning of circumference

## Chapter 2: Reasoning and Proof

### 2.1 Inductive Reasoning

- Solve Toothpick Puzzles!—Easy introduction to reasoning by solving ten puzzles involving 24 toothpicks
- Illuminations: Counting Embedded Figures—Pattern recognition and generalization are the key to this activity

### 2.4 Deductive Reasoning

- Illuminations: Venn Diagrams and Logic—A visual approach at developing different reasoning techniques

### 2.8 Bisectors

- Illuminations: Perpendicular Bisector—Applet shows the concept and construction of a perpendicular bisector
- Illuminations: Angle Bisector—Applet shows the concept and construction of an angle bisector

## Chapter 3: Parallel and Perpendicular Lines

### 3.3 Slopes and Distances in the Coordinate Plane

- Illuminations: Pi Line—Experimental activity that relates the slope of a line to pi

### 3.5 Parallel and Perpendicular Constructions

- Illuminations: Dropping a Perpendicular Line—An applet that demonstrates the perpendicular line construction
- Illuminations: Constructing a Perpendicular Line—An applet that demonstrates the construction of a perpendicular line

### 3.6 Triangle Angle Sum Theorem

- Illuminations: Adding it All Up—Students use paper and pencil as well as dynamic software to study convex and concave polygons and their interior angle measures

## Chapter 4: Congruent Triangles

### 4.1 Triangles and their Angles

- Illuminations: Triangle Classification—Applet and activity sheet helps students see the characteristics of the different types of triangles
- Video on Triangle Classification—This video can be used throughout Chapter 4. Small clips can be used in different lessons.

### 4.3 Congruence Postulates

- Illuminations: Congruence Theorems—Exploratory activity where students determine essential parts of a triangle that guarantees congruency

### 4.4 Congruence Theorems

- Illuminations: Pieces of Proof—Excellent activity as student begin to prove triangles congruent by identifying properties from a diagram and applying postulates and theorems to form a proof

## Chapter 5: Relationships in Triangles

### 5.1 Bisectors in Triangles

- Illuminations: Incircle—Applet showing the meaning and basic construction of an incircle
- Illuminations: Circumcircle—Applet showing the meaning and basic construction of a circumcircle

### 5.2 Medians and Altitudes

- Illuminations: Location, Location, Location—Students work together on this activity as they try to determine the shortest distance between a point in a regular polygon and its sides using an applet
- Illuminations: Median—Applet shows medians and relationship of the side lengths and perimeter
- Illuminations: Euler Line—Applet shows the altitudes and medians as well as a development of the Euler Line

### 5.4 Inequalities within a Triangle

- Illuminations: Inequalities in Triangles- Students see the inequalities in a triangle by using spaghetti to form triangles and discover relationships between side lengths and angle measures and side lengths to side lengths
- Illuminations: Triangle Inequality—Nice applet to show the properties of inequalities of side lengths in a triangle.

### 5.6 Triangle Constructions

- Illuminations: What Does It Take to Construct a Triangle? —Students actively discover and conjecture when triangles can be constructed and when it is impossible depending on the given side lengths

## Chapter 6: Quadrilaterals

- Go on a Geometry Scavenger Hunt—Supply a list of geometric terms that students need to find and photograph

### 6.1 Classifying Quadrilaterals

- Polygon Capture—Through a game students identify and classify polygons

### 6.2 Characteristics of Parallelograms

- Illuminations: Rectangles and Parallelograms—Software is used to explore the relational characteristics between rectangles and parallelograms.
- Illuminations: Diagonals to Quadrilaterals—Investigation of quadrilateral given only their diagonals

### 6.3 Proofs of Parallelograms

- Illuminations: Perplexing Parallelogram—Exploration of line segments parallel to a side of a parallelogram lead to conjecture and proof

### 6.4 Rectangles, Rhombi and Squares

- Illuminations: A Ratio that Glitters: Exploring the Golden Rectangle—Develop an understanding of the Golden Ratio and how to construct a Golden Rectangle

## Chapter 7: Area

### 7.1 Areas of Parallelograms and Triangles

- Illuminations: Interactive Geometry Dictionary: Areas in Geometry—Gives the development of the concept of area of rectangle, parallelogram and triangle

### 7.3 The Pythagorean Theorem

- Illuminations: Corner to Corner: Exploring Diagonals and the Pythagorean Theorem— Investigation starts with diagonals leads to the Pythagorean Theorem and takes a look at irrational numbers
- Science of the NFL Football: Pythagorean Theorem—Application of this famous theorem to find a defenders line of pursuit.

### 7.5 Areas of Regular Polygons

- Illuminations: Pinwheels—Origami style parallelograms and octagons are formed to study angle measure, side lengths and area of polygons

### 7.6 Circles and Arcs

- Illuminations: Circle Packing—Determine efficiency of packing circular objects by looking at circumference and area

### 7.7 Areas of Circles, Sectors and Segments

- Illuminations: Princess Dido and the Ox Skin: Investigating Maximizing Area Using a Literature-Based Model—An enrichment idea that could be used as a final assessment project for this chapter

## Chapter 8: Similarity

### 8.1 Ratios and Proportions

- Illuminations: Measuring Up—Similar figures, ratios and proportions are used in this activity

### 8.2 Similar Polygons

- Illuminations: How Far Can You Go in a New York Minute—Connections between map scales and similarity are shown as well as using SSS to show similarity of triangles

## Chapter 9: Trigonometry

### 9.3 Applications of Trigonometry

- Illuminations: Trigonometry for Solving Problems—Students learn how trigonometry can be used to solve problems with this activity which includes angles of elevation and depression

### 9.4 Vectors

- Science of NHL Hockey: Vectors—Introduces the idea of a vector using a hockey pass
- Science of NFL Football: Vectors—Introduces the idea of a vector using a football pass
- Illuminations: Components of a Vector—An introduction to vectors is given in this lesson with components of magnitude and direction used in the movement of a car
- Illuminations: Sums of Vectors and their Properties—This is a game-like activity where students direct the path of an airplane by using vector sums.
- Illuminations: Vector Investigation—Boat—A boat is moved around in the water by the use of vectors with components representing the rate of the current and boat speed

### 9.5 Area using Trigonometry

- Illuminations: Inscribed and Circumscribed Polygons—An algorithm is developed to compute the digits of p by investigating inscribed and circumscribed polygons around a unit circle

### 9.7 Law of Sines and Law of Cosines

- Illuminations: Squares on a Triangle—Students see the connection between the Pythagorean Theorem and the Law of Cosines by look at the area of squares on the sides of a right triangle
- Illuminations: Law of Sines—Students develop the Law of Sines using right-triangle trigonometry concepts
- Illuminations: Law of Sines and Law of Cosines—Emphasis of this lesson is an introduction to the Law of Sines and Cosines and practice in determining which one to use in a variety of situations

## Chapter 10: Circles

### 10.1 Circles and Chords

- Illuminations: Circle Tool—Provides a general review of circles and their parts using both a MIRA and dynamic software
- Illuminations: Power of Points—Interesting site investigates the intersection of chords, tangent lines and secant lines using the soccer problem applet

### 10.3 Arcs

- Illuminations: Folding Circles: Exploring Circle Theorems through Paper Folding— Students are introduced to some of the basic theorems about circles involving arcs, central angles and inscribed angles through paper folding

## Chapter 11: Surface Area and Volume

### 11.2 Tetrahedral Kites

- Illuminations: Tetrahedral Kites—Detailed description of an end of class project where students build a three dimensional figure made of straws and tissue paper

### 11.3 Surface Areas of Prisms and Cylinders

- Illuminations: Soda Cans—Students determine the most efficient way to create a six- or twelve-pack of soda in a real-life application of geometry

## Chapter 12: Transformations and Symmetry

### 12.3 Rotations

- Illuminations: Flip-n-Slide: Exploring Transformations through Modeling and Computer Games—A two-day lesson on translations, reflections and rotations

### 12.5 Symmetry

- Illuminations: Relationships between Reflections and Symmetry—The connection between reflections and symmetry is developed through the activities at this site
- Explore Symmetry: Draw the Other Half—Use photos or magazine pictures to explore symmetry

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