I: Students will use algebraic, spatial, and logical reasoning to solve geometry problems.

I.1: Use inductive and deductive reasoning to develop mathematical arguments.

I.1.a: Write conditional statements, converses, and inverses, and determine the truth value of these statements.

 Biconditional Statements
 Conditional Statements

I.1.c: Prove a statement false by using a counterexample.

 Conditional Statements

I.2: Analyze characteristics and properties of angles.

I.2.b: Identify and determine relationships in adjacent, complementary, supplementary, or vertical angles and linear pairs.

 Investigating Angle Theorems
 Triangle Angle Sum

I.2.d: Prove relationships in angle pairs.

 Investigating Angle Theorems
 Triangle Angle Sum

I.3: Analyze characteristics and properties of triangles.

I.3.a: Prove congruency and similarity of triangles using postulates and theorems.

 Congruence in Right Triangles
 Proving Triangles Congruent
 Similar Figures

I.3.b: Prove the Pythagorean Theorem in multiple ways, find missing sides of right triangles using the Pythagorean Theorem, and determine whether a triangle is a right triangle using the converse of the Pythagorean Theorem.

 Cosine Function
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine Function
 Tangent Function

I.3.c: Prove and apply theorems involving isosceles triangles.

 Isosceles and Equilateral Triangles
 Triangle Inequalities

I.3.d: Apply triangle inequality theorems.

 Triangle Inequalities

I.3.e: Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle, and justify the concurrency theorems.

 Concurrent Lines, Medians, and Altitudes
 Similarity in Right Triangles

I.4: Analyze characteristics and properties of polygons and circles.

I.4.a: Use examples and counterexamples to classify subsets of quadrilaterals.

 Classifying Quadrilaterals
 Parallelogram Conditions
 Special Parallelograms

I.4.b: Prove properties of quadrilaterals using triangle congruence relationships, postulates, and theorems.

 Parallelogram Conditions
 Special Parallelograms

I.4.c: Derive, justify, and use formulas for the number of diagonals, lines of symmetry, angle measures, perimeter, and area of regular polygons.

 Area of Triangles

I.4.d: Define radius, diameter, chord, secant, arc, sector, central angle, inscribed angle, and tangent of a circle, and solve problems using their properties.

 Inscribed Angles

I.4.e: Show the relationship between intercepted arcs and inscribed or central angles, and find their measures.

 Chords and Arcs
 Inscribed Angles

I.5: Perform basic geometric constructions, describing and justifying the procedures used.

I.5.a: Investigate geometric relationships using constructions.

 Segment and Angle Bisectors

I.5.b: Copy and bisect angles and segments.

 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines
 Segment and Angle Bisectors

I.5.c: Construct perpendicular and parallel lines.

 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines
 Parallel, Intersecting, and Skew Lines

I.5.e: Discover and investigate conjectures about geometric properties using constructions.

 Segment and Angle Bisectors

I.6: Analyze characteristics and properties of three-dimensional figures.

I.6.a: Identify and classify prisms, pyramids, cylinders and cones based on the shape of their base(s).

 Pyramids and Cones

II: Students will use the language and operations of algebra to explore geometric relationships with coordinate geometry.

II.1: Describe the properties and attributes of lines and line segments using coordinate geometry.

II.1.b: Find the distance between two given points and find the coordinates of the midpoint.

 Points in the Coordinate Plane

II.a: Graph a circle given the equation in the form(x − h)2 + (y − k)2 = r 2 , and write the equation when given the graph.

 Circles

II.b: Determine whether points in a set are collinear.

 Slope

III: Students will extend concepts of proportion and similarity to trigonometric ratios.

III.1: Use triangle relationships to solve problems.

III.1.a: Solve problems using the properties of special right triangles, e.g., 30°, 60°, 90° or 45°, 45°, 90°.

 Cosine Function
 Sine Function
 Tangent Function

III.1.b: Identify the trigonometric relationships of sine, cosine, and tangent with the appropriate ratio of sides of a right triangle.

 Cosine Function
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Tangent Function

III.2: Use the trigonometric ratios of sine, cosine, and tangent to represent and solve for missing parts of triangles.

III.2.a: Find the angle measure in degrees when given the trigonometric ratio.

 Cosine Function
 Sine Function
 Tangent Function

III.2.c: Find unknown measures of right triangles using sine, cosine, and tangent functions and inverse trigonometric functions.

 Cosine Function
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Sum and Difference Identities for Sine and Cosine
 Tangent Function

IV: Students will use algebraic, spatial, and logical reasoning to solve measurement problems.

IV.1: Find measurements of plane and solid figures.

IV.1.a: Find linear and angle measures in real-world situations using appropriate tools or technology.

 Similar Figures

IV.1.b: Develop surface area and volume formulas for polyhedra, cones, and cylinders.

 Prisms and Cylinders
 Pyramids and Cones
 Surface and Lateral Areas of Prisms and Cylinders
 Surface and Lateral Areas of Pyramids and Cones

IV.1.c: Determine perimeter, area, surface area, lateral area, and volume for prisms, cylinders, pyramids, cones, and spheres when given the formulas.

 Circumference and Area of Circles
 Perimeter and Area of Rectangles
 Perimeters and Areas of Similar Figures
 Prisms and Cylinders
 Pyramids and Cones
 Surface and Lateral Areas of Prisms and Cylinders
 Surface and Lateral Areas of Pyramids and Cones

IV.2: Solve real-world problems using visualization and spatial reasoning.

IV.2.a: Solve problems using the Pythagorean Theorem and its converse.

 Circles
 Cosine Function
 Distance Formula
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Sine Function
 Surface and Lateral Areas of Pyramids and Cones
 Tangent Function

IV.2.b: Solve problems using the distance formula.

 Circles
 Distance Formula

IV.2.c: Solve problems involving trigonometric ratios.

 Cosine Function
 Sine Function
 Sine, Cosine, and Tangent Ratios
 Tangent Function

IV.2.d: Solve problems involving geometric probability.

 Geometric Probability

Correlation last revised: 1/20/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.