Shared Gizmo List: Illinois HS Math - Geometry

Gizmos aligned to Illinois HS - Geometry standards
Algebra IAlgebra IIGeometry

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Shared by an elementary school math and science teacher.

Congruence

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.
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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.
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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.
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Rotations, Reflections, and Translations Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
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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.
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Dilations 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.
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Translations Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
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Proving Triangles Congruent Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence.
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Investigating Angle Theorems Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
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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.
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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.
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Triangle Inequalities 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.
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Parallelogram Conditions Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram.
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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?
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Similarity, Right Triangles, and Trigonometry

Similar Figures 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.
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Dilations 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.
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Perimeters and Areas of Similar Figures Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare.
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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.
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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.
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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.
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Distance Formula 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 examine changes to the triangle and the distance calculation.
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Circles

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.
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Inscribed Angles Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept.
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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.
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Expressing Geometric Properties with Equations

Distance Formula 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 examine changes to the triangle and the distance calculation.
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Pythagorean Theorem with a Geoboard Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem.
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Parabolas Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation.
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Ellipses Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property.
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Hyperbolas Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response.
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Geometric Measurement and Dimension

Circumference and Area of Circles Resize a circle and compare its radius, circumference, and area.
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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.
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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.
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