2: The student will demonstrate the ability to solve mathematical and real-world problems using measurement and geometric models and will justify solutions and explain processes used.

2.1: The student will represent and analyze two- and three-dimensional figures using tools and technology when appropriate.

2.1.1: The student will analyze the properties of geometric figures.

2.1.1.A: Essential properties, relationships, and geometric models include the following:

2.1.1.A.a: congruence and similarity

Classifying Quadrilaterals - Activity B
Congruence in Right Triangles
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons
Special Quadrilaterals

2.1.1.A.b: line/segment/plane relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)

Concurrent Lines, Medians, and Altitudes

2.1.1.A.d: angles and angle relationships (vertical, adjacent, complementary, supplementary, obtuse, acute, right, interior, exterior)

Investigating Angle Theorems - Activity A
Triangle Angle Sum - Activity A

2.1.1.A.e: angle relationships with parallel lines

Investigating Angle Theorems - Activity A

2.1.1.A.f: polygons (regular, non-regular, composite, equilateral, equiangular)

Classifying Triangles
Isosceles and Equilateral Triangles
Parallelogram Conditions
Special Quadrilaterals
Triangle Angle Sum - Activity A

2.1.1.A.g: geometric solids (cones, cylinders, prisms, pyramids, composite figures)

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

2.1.1.A.h: circle/sphere (tangent, radius, diameter, chord, secant, central/inscribed angle, inscribed, circumscribed).

Chords and Arcs
Inscribing Angles

2.1.1.1: The student will recognize geometric solids when given the two-dimensional

Surface and Lateral Area of Pyramids and Cones

2.1.1.2: The student will draw two-dimensional representations of three-dimensional solids.

3D and Orthographic Views - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

2.1.1.3: The student will analyze the properties and relationships of geometric solids with bases other than rectangles, triangles, or circles.

Prisms and Cylinders - Activity A

2.1.1.4: The student will analyze the properties and relationships of oblique solids.

Prisms and Cylinders - Activity A
Pyramids and Cones - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

2.1.1.5: The student will analyze the properties and relationships of truncated three-dimensional solids.

Prisms and Cylinders - Activity A

2.1.1.6: The student will explore the relationship between the measure of the central angle and the arc length in a circle.

Chords and Arcs

2.1.2: The student will identify and/or verify properties of geometric figures using the coordinate plane and concepts from algebra.

2.1.2.A: ?Verify properties? means to justify solutions using definitions and/or mathematical principles.

Simplifying Trigonometric Expressions

2.1.2.B: Properties, relationships, and geometric models include the following:

2.1.2.B.a: congruence and similarity

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

2.1.2.B.b: line/segment relationships (parallel, perpendicular, intersecting, bisecting, midpoint, median, altitude)

Concurrent Lines, Medians, and Altitudes
Construct Parallel and Perpendicular Lines

2.1.2.B.d: angles and angle relationships (obtuse, acute, right)

Classifying Triangles

2.1.2.B.e: polygons (regular, non-regular, equilateral, equiangular)

Classifying Triangles
Isosceles and Equilateral Triangles
Parallelogram Conditions
Special Quadrilaterals
Triangle Angle Sum - Activity A

2.1.2.B.f: circle (tangent, radius, diameter, chord).

Chords and Arcs
Tangent Ratio

2.1.2.D: Concepts from algebra include applications of the distance, midpoint, and slope formulas.

Slope - Activity B

2.1.2.1: The student will locate points on the polar coordinate system including points with rotation greater than 360°.

Points in Polar Coordinates

2.1.2.2: The student will explore the relationship between a point on the coordinate plane with the same point on the polar coordinate system.

Points in Polar Coordinates

2.1.2.4: The student will use the distance and midpoint formulas for segments in three-dimensional space.

Distance Formula - Activity A

2.1.3: The student will use transformations to move figures, create designs, and/or demonstrate geometric properties.

2.1.3.A: Transformations include reflections, rotations, translations, and dilations.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

2.1.3.B: Items should go beyond the identification of transformations.

Dilations
Reflections
Rotations, Reflections and Translations

2.1.3.C: Essential properties and relationships include the following: congruence, similarity, and symmetry.

Congruence in Right Triangles
Holiday Snowflake Designer
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

2.1.3.D: The student?s explanation of a transformation must include the following:

2.1.3.D.a: translation ? distance and direction

Translations

2.1.3.D.b: reflection ? line of reflection

Reflections

2.1.3.D.d: dilation ? center and scale factor.

Dilations

2.1.3.E: Paper folding and the use of Miras? and mirrors are appropriate methods for performing transformations, and their use must be referenced.

Dilations
Reflections
Rotations, Reflections and Translations

2.1.3.a: Given one or more transformations, the student sketches the result of the transformation(s) and/or explains the geometric effect of the transformation(s) on the figure.

Dilations
Reflections
Rotations, Reflections and Translations

2.1.3.2: The student will find transformation images, including rotations, reflections, dilations and translations, using matrices.

Dilations
Reflections
Rotations, Reflections and Translations
Translations

2.1.3.3: The student will identify the distance and direction of a given vector.

Adding Vectors
Vectors

2.1.3.4: The student will find resultant vectors.

Adding Vectors
Vectors

2.1.3.5: The student will describe translations using vectors.

Adding Vectors
Translations
Vectors

2.1.3.6: The student will find translation images using vector sums.

Adding Vectors
Rotations, Reflections and Translations
Translations
Vectors

2.1.4: The student will construct and/or draw and/or validate properties of geometric figures using appropriate tools and technology.

2.1.4.A: ?Validate properties? in this indicator, means justifying solutions using definitions, mathematical principles and/or measurement.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

2.1.4.B: Students may use a compass, straightedge, patty paper, a Mira?, and/or a mirror as construction tools. Using a ruler or protractor cannot be part of the strategy.

Classifying Quadrilaterals - Activity B
Construct Parallel and Perpendicular Lines
Parallelogram Conditions
Special Quadrilaterals

2.1.4.C: Students may use a compass, ruler, patty paper, a Mira?, a mirror and/or a protractor as drawing tools.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

2.1.4.D: It is acceptable to do a construction when the item asks for a drawing.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

2.1.4.E: Paper folding and the use of Miras? and mirrors are appropriate methods for representing, constructing, and/or analyzing figures, and their use must be referenced.

Classifying Quadrilaterals - Activity B
Parallelogram Conditions
Special Quadrilaterals

2.1.4.F: Constructions and drawings are limited to the two-dimensional relationships listed in 2.1.1.

Classifying Quadrilaterals - Activity B
Classifying Triangles
Parallelogram Conditions
Polygon Angle Sum - Activity A
Special Quadrilaterals

2.2: The student will apply geometric properties and relationships to solve problems using tools and technology when appropriate.

2.2.1: The student will identify and/or verify congruent and similar figures and/or apply equality or proportionality of their corresponding parts.

2.2.1.A: Students will demonstrate geometric reasoning and justify conclusions. Although the focus is on geometric theory, answers to some items may include a numeric answer.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

2.2.1.B: Corresponding measurements include length, angle measure, perimeter, circumference, area, volume, surface area and lateral area.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Perimeters and Areas of Similar Figures
Rectangle: Perimeter and Area

2.2.1.a: The student recognizes shapes as congruent or similar, calculates corresponding measurements, and/or justifies conclusions.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A
Similar Polygons

2.2.1.b: The student uses congruency and similarity statements to identify corresponding parts of figures.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

2.2.2: The student will solve problems using two-dimensional figures and/or right-triangle trigonometry.

2.2.2.A: Students will demonstrate geometric reasoning and justify conclusions.

Sine and Cosine Ratios - Activity A

2.2.2.B: Trigonometric functions may be used to find sides or angles.

Sine and Cosine Ratios - Activity A

2.2.2.C: Trigonometric functions will be limited to sine, cosine, and tangent and their inverses.

Sine and Cosine Ratios - Activity A
Sine, Cosine and Tangent
Tangent Ratio

2.2.2.a: The student solves a problem involving missing parts of two-dimensional figures, which may require the use of right-triangle trigonometry, the Pythagorean theorem, or special right triangle relationships.

Distance Formula - Activity A
Geoboard: The Pythagorean Theorem
Pythagorean Theorem - Activity A
Pythagorean Theorem - Activity B
Sine and Cosine Ratios - Activity A

2.2.2.3: The student will use geometric mean and relationships between parts of a right triangle and the altitude drawn to the hypotenuse to find missing parts of right triangles.

Similarity in Right Triangles

2.3: The student will apply concepts of measurement using tools and technology when appropriate.

2.3.1: The student will use algebraic and/or geometric properties to measure indirectly.

2.3.1.A: ?Measure indirectly? means to use mathematical concepts such as congruence, similarity, and ratio and proportion to calculate measurements.

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

2.3.1.B: Similarity and congruence will be directly stated or implied (scale drawings, enlargements.)

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Similar Figures - Activity A
Similar Polygons

2.3.2: The student will use techniques of measurement and will estimate, calculate, and/or compare perimeter, circumference, area, volume, and/or surface area of two- and three-dimensional figures and their parts.

2.3.2.A: Two-dimensional shapes include polygons, circles, and composite figures.

Area of Parallelograms - Activity A
Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B

2.3.2.B: Three-dimensional shapes include cubes, prisms, pyramids, cylinders, cones, spheres, and composite figures.

Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders
Surface and Lateral Area of Pyramids and Cones

2.3.2.C: Formulas will be provided.

Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Prisms and Cylinders - Activity A
Rectangle: Perimeter and Area
Surface and Lateral Area of Prisms and Cylinders

2.3.2.D: No oblique solids will be used.

Prisms and Cylinders - Activity A
Surface and Lateral Area of Prisms and Cylinders

2.3.2.E: Items may involve applications of geometric properties and relationships.

Classifying Triangles
Parallelogram Conditions
Polygon Angle Sum - Activity A
Prisms and Cylinders - Activity A
Special Quadrilaterals
Triangle Angle Sum - Activity A

2.3.2.a: The student solves a problem involving perimeter, area, surface area, lateral area, circumference, and/or volume expressing solutions with appropriate units.

Circle: Circumference and Area
Minimize Perimeter
Perimeter, Circumference, and Area - Activity B
Rectangle: Perimeter and Area

2.3.2.3: The student will determine properties of oblique solid geometric figures.

Prisms and Cylinders - Activity A

2.3.2.4: The student will determine properties of pyramids that have non-square bases.

Pyramids and Cones - Activity A