LG.1.G: Students will develop the language of geometry including specialized vocabulary, reasoning, and application of theorems, properties, and postulates.

LG.1.G.1: Define, compare and contrast inductive reasoning and deductive reasoning for making predictions based on real world situations

LG.1.G.1.c: conditional statements (statement, inverse, converse, and contrapositive)

 Biconditional Statements
 Conditional Statements

LG.1.G.3: Describe relationships derived from geometric figures or figural patterns

 Finding Patterns

LG.1.G.4: Apply, with and without appropriate technology, definitions, theorems, properties, and postulates related to such topics as complementary, supplementary, vertical angles, linear pairs, and angles formed by perpendicular lines

 Constructing Congruent Segments and Angles
 Constructing Parallel and Perpendicular Lines
 Investigating Angle Theorems
 Triangle Angle Sum

LG.1.G.5: Explore, with and without appropriate technology, the relationship between angles formed by two lines cut by a transversal to justify when lines are parallel

 Constructing Congruent Segments and Angles
 Triangle Angle Sum

LG.1.G.6: Give justification for conclusions reached by deductive reasoning. State and prove key basic theorems in geometry (i.e., the Pythagorean theorem, the sum of the measures of the angles of a triangle is 180° , and the line joining the midpoints of two sides of a triangle is parallel to the third side and half it?s length

 Conditional Statements
 Investigating Angle Theorems
 Isosceles and Equilateral Triangles
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Triangle Angle Sum

T.2.G: Students will identify and describe types of triangles and their special segments. They will use logic to apply the properties of congruence, similarity, and inequalities. The students will apply the Pythagorean Theorem and trigonometric ratios to solve problems in real world situations.

T.2.G.1: Apply congruence (SSS ?) and similarity (AA...) correspondences and properties of figures to find missing parts of geometric figures and provide logical justification

 Circles
 Constructing Congruent Segments and Angles
 Perimeters and Areas of Similar Figures
 Similar Figures
 Similarity in Right Triangles

T.2.G.2: Investigate the measures of segments to determine the existence of triangles (triangle inequality theorem)

 Triangle Inequalities

T.2.G.3: Identify and use the special segments of triangles (altitude, median, angle bisector, perpendicular bisector, and midsegment) to solve problems

 Classifying Triangles
 Concurrent Lines, Medians, and Altitudes
 Similarity in Right Triangles

T.2.G.4: Apply the Pythagorean Theorem and its converse in solving practical problems

 Circles
 Distance Formula
 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard
 Surface and Lateral Areas of Pyramids and Cones

T.2.G.5: Use the special right triangle relationships (30°-60°-90° and 45°-45°-90°) to solve problems

 Cosine Function
 Sine Function
 Tangent Function

T.2.G.6: Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression

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

T.2.G.7: Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given including angles of elevation and angles of depression

 Sine, Cosine, and Tangent Ratios

M.3.G: Students will measure and compare, while using appropriate formulas, tools, and technology to solve problems dealing with length, perimeter, area and volume.

M.3.G.1: Calculate probabilities arising in geometric contexts

 Geometric Probability

M.3.G.2: Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms

 Area of Parallelograms
 Area of Triangles
 Perimeter and Area of Rectangles
 Prisms and Cylinders
 Pyramids and Cones
 Surface and Lateral Areas of Prisms and Cylinders
 Surface and Lateral Areas of Pyramids and Cones

M.3.G.4: Use (given similar geometric objects) proportional reasoning to solve practical problems (including scale drawings)

 Beam to Moon (Ratios and Proportions)
 Dilations

R.4.G: Students will analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

R.4.G.1: Explore and verify the properties of quadrilaterals

 Classifying Quadrilaterals
 Parallelogram Conditions
 Special Parallelograms

R.4.G.2: Solve problems using properties of polygons:

R.4.G.2.a: sum of the measures of the interior angles of a polygon

 Polygon Angle Sum
 Triangle Angle Sum

R.4.G.2.b: interior and exterior angle measure of a regular polygon or irregular polygon

 Polygon Angle Sum

R.4.G.2.c: number of sides or angles of a polygon

 Polygon Angle Sum

R.4.G.5: Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

 Chords and Arcs
 Inscribed Angles

R.4.G.6: Solve problems using inscribed and circumscribed figures

 Concurrent Lines, Medians, and Altitudes
 Inscribed Angles

R.4.G.7: Use orthographic drawings (top, front, side) and isometric drawings (corner) to represent three-dimensional objects

 3D and Orthographic Views

CGT.5.G: Students will specify locations, apply transformations and describe relationships using coordinate geometry.

CGT.5.G.1: Use coordinate geometry to find the distance between two points, the midpoint of a segment, and the slopes of parallel, perpendicular, horizontal, and vertical lines

 Point-Slope Form of a Line

CGT.5.G.6: Write, in standard form, the equation of a circle given a graph on a coordinate plane or the center and radius of a circle

 Circles

CGT.5.G.7: Draw and interpret the results of transformations and successive transformations on figures in the coordinate plane

CGT.5.G.7.a: translations

 Rotations, Reflections, and Translations
 Translations

CGT.5.G.7.b: reflections

 Reflections
 Rotations, Reflections, and Translations

CGT.5.G.7.c: rotations (90°, 180°, clockwise and counterclockwise about the origin)

 Dilations
 Rotations, Reflections, and Translations

CGT.5.G.7.d: dilations (scale factor)

 Dilations
 Similar Figures

Correlation last revised: 5/8/2018

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