Core Curriculum

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.

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.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.

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.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.

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.

Chords and Arcs

Inscribed Angles

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

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.

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

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

Points in the Coordinate Plane

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.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.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.

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.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.

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.

Correlation last revised: 4/4/2018

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