### 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.

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

#### 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.

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

#### I.3: Analyze characteristics and properties of triangles.

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

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.

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

I.3.d: Apply triangle inequality theorems.

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.

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

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

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

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

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.

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

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

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

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

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

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

#### 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).

### 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.

### 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°.

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

#### 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.

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

### 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.

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

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

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

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

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

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

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

Correlation last revised: 5/24/2018

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