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