Geometry (2004)
Chapter 1. Tools of Geometry
1-1. Patterns and Inductive Reasoning
Finding Patterns
Build a pattern to complete a sequence of patterns. Study a sequence of three patterns of squares in a grid and build the fourth pattern of the sequence in a grid. 5 Minute Preview
1-2. Points, Lines, and Planes
Parallel, Intersecting, and Skew Lines
Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of these objects. 5 Minute Preview
1-3. Segments, Rays, Parallel Lines and Planes
Parallel, Intersecting, and Skew Lines
Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of these objects. 5 Minute Preview
1-5. Basic Constructions
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
Constructing Congruent Segments and Angles
Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
1-6. The Coordinate Plane
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
1-7. Perimeter, Circumference and Area
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
Perimeter and Area of Rectangles
Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle). 5 Minute Preview
Chapter 2. Reasoning and Proof
2-1. Conditional Statements
Conditional Statements
Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
2-2. Biconditionals and Definitions
Biconditional Statements
Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview
2-5. Proving Angles Congruent
Investigating Angle Theorems
Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview
Chapter 3. Parallel and Perpendicular Lines
3-3. Parallel Lines and the Triangle Angle-Sum Theorem
Triangle Angle Sum
Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures. 5 Minute Preview
3-4. The Polygon Angle-Sum Theorems
Polygon Angle Sum
Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged. 5 Minute Preview
3-5. Lines in the Coordinate Plane
Slope-Intercept Form of a Line
Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Point-Slope Form of a Line
Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
Standard Form of a Line
Compare the standard form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response. 5 Minute Preview
3-7. Constructing Parallel and Perpendicular Lines
Constructing Parallel and Perpendicular Lines
Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction. 5 Minute Preview
Chapter 4. Congruent Triangles
4-2. Triangle Congruence by SSS and SAS
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4-3. Triangle Congruence by ASA and AAS
Proving Triangles Congruent
Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence. 5 Minute Preview
4-5. Isosceles and Equilateral Triangles
Isosceles and Equilateral Triangles
Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview
4-6. Congruence in Right Triangles
Congruence in Right Triangles
Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent. 5 Minute Preview
Chapter 5. Relationships Within Triangles
5-2. Bisectors in Triangles
Segment and Angle Bisectors
Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true. 5 Minute Preview
5-3. Concurrent Lines, Medians, and Altitudes
Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview
5-4. Inverses, Contrapositives, and Indirect Reasoning
Concurrent Lines, Medians, and Altitudes
Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped. 5 Minute Preview
Chapter 6. Quadrilaterals
6-1. Classifying Quadrilaterals
Classifying Quadrilaterals
Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals. 5 Minute Preview
6-3. Proving That a Quadrilateral is a Parallelogram
Parallelogram Conditions
Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram. 5 Minute Preview
6-4. Special Parallelograms
Special Parallelograms
Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition? 5 Minute Preview
6-6. Placing Figures in the Coordinate Plane
Points in the Coordinate Plane
Identify the coordinates of a point in the coordinate plane. Drag the point in the plane and investigate how the coordinates change in response. 5 Minute Preview
Chapter 7. Area
7-1. Areas of Parallelograms and Triangles
Area of Triangles
Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles. 5 Minute Preview
7-2. The Pythagorean Theorem and Its Converse
Pythagorean Theorem
Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle. 5 Minute Preview
7-6. Circles and Arcs
Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
7-7. Areas of Circles and Sectors
Circumference and Area of Circles
Resize a circle and compare its radius, circumference, and area. 5 Minute Preview
7-8. Geometric Probability
Geometric Probability
Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it 5 Minute Preview
Chapter 8. Similarity
8-1. Ratios and Proportions
Part-to-part and Part-to-whole Ratios
Compare a ratio represented by an area with its percent, fraction, and decimal forms. 5 Minute Preview
8-4. Similarity in Right Triangles
Similarity in Right Triangles
Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles. 5 Minute Preview
Chapter 9. Right Triangle Trigonometry
9-1. The Tangent Ratio
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
9-2. Sine and Cosine Ratios
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
Sine, Cosine, and Tangent Ratios
Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change. 5 Minute Preview
9-4. Vectors
Adding Vectors
Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation. 5 Minute Preview
Chapter 10. Surface Area and Volume
10-2. Space Figures and Drawings
3D and Orthographic Views
Arrange blocks in a three-dimensional space so that the top view, front view, and side view match the target top view, front view, and side view. 5 Minute Preview
10-3. Surface Areas and Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders
Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
10-4. Surface Areas of Pyramids and Cones
Surface and Lateral Areas of Pyramids and Cones
Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid. 5 Minute Preview
10-5. Volumes of Prisms and Cylinders
Prisms and Cylinders
Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder. 5 Minute Preview
10-6. Volumes of Pyramids and Cones
Pyramids and Cones
Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone. 5 Minute Preview
Chapter 11. Circles
11-2. Chords and Arcs
Chords and Arcs
Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center. 5 Minute Preview
11-3. Inscribed Angles
Inscribed Angles
Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept. 5 Minute Preview
11-5. Circles in the Coordinate Plane
Circles
Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response. 5 Minute Preview
Chapter 12. Transformations
12-1. Reflections
Reflections
Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated. 5 Minute Preview
12-2. Translations
Translations
Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview
12-3. Rotations
Rotations, Reflections, and Translations
Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview
12-7. Dilations
Dilations
Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in
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