Browse by Grade & Topic: Geometry

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.

Resize a circle and compare its radius, circumference, and area.

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As factory belt operator, your job is to move boxes just the right distance on the belt, so they can be stamped for delivery. Your only controls are the radius and rotation of the belt’s...

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.

Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept.

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...

Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction.

Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction.

Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.

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...

Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form.

Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form.

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...

Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of...

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...

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).

Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation.

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.

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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.

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.

Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram.

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...

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?

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...

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.

Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles.

Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence.

Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles.

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...

Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles.

Place constraints on a triangle and determine what classifications must apply to the triangle.

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form.

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.

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.

Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.

Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related.

Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation.

Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and...

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.

Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem.

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.

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.

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...

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...