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# Oklahoma - Mathematics: Geometry

## OK--Academic Standards | Adopted: 2016

### G.RL: : Geometry: Reasoning & Logic

G.RL.1: : Use appropriate tools and logic to evaluate mathematical arguments.

G.RL.1.1: : Understand the use of undefined terms, definitions, postulates, and theorems in logical arguments/proofs.

Biconditional Statements

Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview

Investigating Angle Theorems

Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure. 5 Minute Preview

Isosceles and Equilateral Triangles

Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles. 5 Minute Preview

G.RL.1.2: : Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. Recognize the logical relationships between a conditional statement and its inverse, converse, and contrapositive.

Biconditional Statements

Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview

Conditional Statements

Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview

G.RL.1.3: : Assess the validity of a logical argument and give counterexamples to disprove a statement.

Biconditional Statements

Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form. 5 Minute Preview

Conditional Statements

Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form. 5 Minute Preview

### G.2D: : Geometry: Two-Dimensional Shapes

G.2D.1: : Discover, evaluate and analyze the relationships between lines, angles, and polygons to solve real-world and mathematical problems; express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts, or illustrations.

G.2D.1.1: : Apply the properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve real-world and mathematical problems and determine if two lines are parallel, using algebraic reasoning and proofs.

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

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

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

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

G.2D.1.2: : Apply the properties of angles, including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve real-world and mathematical problems using algebraic reasoning and proofs.

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

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

G.2D.1.4: : Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) and use them to solve real-world and mathematical problems involving angle measures and segment lengths using algebraic reasoning and proofs.

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

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

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

G.2D.1.5: : Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments.

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

G.2D.1.6: : Apply the properties of polygons to solve real-world and mathematical problems involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures).

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

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. 5 Minute Preview

G.2D.1.8: : Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL) and triangle similarity (AA, SSS, SAS).

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

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

G.2D.1.9: : Use numeric, graphic and algebraic representations of transformations in two dimensions, such as reflections, translations, dilations, and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate plane and identify types of symmetry.

Dilations

Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in

Rotations, Reflections, and Translations

Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure. 5 Minute Preview

Translations

Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation. 5 Minute Preview

### G.3D: : Geometry: Three-Dimensional Shapes

G.3D.1: : Solve real-world and mathematical problems involving three-dimensional figures.

G.3D.1.1: : Solve real-world and mathematical problems using the surface area and volume of prisms, cylinders, pyramids, cones, spheres, and composites of these figures. Use nets, measuring devices, or formulas as appropriate.

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

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

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

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

### G.C: : Geometry: Circles

G.C.1: : Solve real-world and mathematical problems using the properties of circles.

G.C.1.3: : Recognize and write the radius r, center (h, k), and standard form of the equation of a circle (x − h)² + (y − k)² = r² with and without graphs.

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

G.C.1.4: : Apply the distance and midpoint formula, where appropriate, to develop the equation of a circle in standard form.

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

### G.RT: : Geometry: Right Triangle Trigonometry

G.RT.1: : Develop and verify mathematical relationships of right triangles and trigonometric ratios to solve real-world and mathematical problems.

G.RT.1.4: : Apply the trigonometric functions as ratios (sine, cosine, and tangent) to find side lengths in right triangles in real-world and mathematical problems.

Cosine Function

Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle. 5 Minute Preview

Sine Function

Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle. 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

Tangent Function

Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle. 5 Minute Preview

Correlation last revised: 9/16/2020

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