CCSS BY LESSON

1. Basics of Geometry

1.1 Basic Geometric Definitions - CCSS Standard: G-CO.A.1
Define and apply basic geometric terms such as points, lines, angles, and shapes, establishing a foundation in geometry to understand the properties and relationships of geometric figures.

1.2 Distance Between Two Points - CCSS Standard: G-GPE.B.7
Calculate the distance between two points in the coordinate plane using various methods like the Pythagorean Theorem, analyzing spatial relationships between points and understanding distance formulas in geometry.

1.3 Congruent Angles and Angle Bisectors - CCSS Standard: G-CO.A.2
Explore congruent angles and angle bisectors, identifying angles with equal measures and lines that divide angles into two equal parts, applying these concepts in geometric constructions and proofs.

1.4 Midpoints and Segment Bisectors - CCSS Standard: G-GPE.B.4
Understand midpoints and segment bisectors in geometric figures, identifying points that divide line segments into two equal parts and analyzing the properties of these elements in various geometric contexts.

1.5 Angle Measurement - CCSS Standard: G-SRT.C.6
Measure and compare angles using degrees and radians, understanding angular measurement in circles and applying trigonometric ratios to solve problems involving angles in geometric situations.

1.6 Angle Classification - CCSS Standard: G-CO.A.3
Classify angles based on their measures and relationships, categorizing angles as acute, obtuse, right, or straight angles, and understanding angle properties to analyze geometric configurations.

1.7 Complementary Angles - CCSS Standard: G-CO.A.2
Identify and calculate complementary angles, recognizing angle pairs that sum up to 90 degrees and applying the concept of complementary angles in geometric reasoning and proofs.

1.8 Supplementary Angles - CCSS Standard: G-CO.A.2
Recognize and compute supplementary angles, determining angle pairs that add up to 180 degrees and utilizing properties of supplementary angles in geometric constructions and problem-solving.

1.9 Linear Pairs - CCSS Standard: G-CO.A.3
Explore and analyze linear pairs of angles, understanding adjacent angles that form a straight line and applying the properties of linear pairs in angle relationships within geometric figures and proofs.

1.10 Vertical Angles - CCSS Standard: G-CO.A.3
Identify and analyze vertical angles, recognizing pairs of non-adjacent angles formed by intersecting lines and understanding the properties of vertical angles in geometric constructions and arguments.

1.11 Triangle Classification - CCSS Standard: G-SRT.B.5
Classify triangles based on their sides and angles, identifying properties of equilateral, isosceles, scalene, acute, obtuse, and right triangles, and analyzing triangle characteristics in geometric proofs and problems.

1.12 Polygon Classification - CCSS Standard: G-CO.A.3
Classify polygons based on the number of sides and angles, categorizing polygons such as triangles, quadrilaterals, pentagons, and so on, and understanding the properties of different types of polygons in geometry and proofs.

2. Reasoning and Proof

2.1 Inductive Reasoning from Patterns - CCSS Standard: F-BF.A.1
Apply inductive reasoning to analyze patterns in functions and make conjectures based on observed data, developing critical thinking skills in the context of mathematical functions to generalize patterns and relationships.

2.2 Deductive Reasoning - CCSS Standard: G-GPE.B.6
Employ deductive reasoning to draw logical conclusions based on geometric principles and theorems, constructing valid arguments and proofs to justify geometric statements and problem solutions.

2.3 If-Then Statements - CCSS Standard: G-CO.A.2
Formulate and evaluate if-then statements in geometric settings, understanding conditional statements and their implications in geometric constructions and proofs to establish logical reasoning in geometry.

2.4 Converse, Inverse, and Contrapositive - CCSS Standard: G-CO.A.2
Analyze the converse, inverse, and contrapositive of conditional statements in geometry, exploring the relationships between these statements and enhancing logical argumentation skills in geometric reasoning.

2.5 Conjectures and Counterexamples - CCSS Standard: G-GPE.B.5
Develop conjectures based on geometric observations and validate them using counterexamples, refining reasoning skills by evaluating geometric statements and providing logical justifications in geometric contexts.

2.6 Properties of Equality and Congruence - CCSS Standard: G-CO.A.12
Investigate properties of equality and congruence in geometric figures, understanding the relationships between equalities and congruences to prove geometric theorems and properties effectively in geometric arguments.

2.7 Two-Column Proofs - CCSS Standard: G-CO.D.12
Construct two-column proofs to demonstrate logical reasoning and justification in geometric arguments and geometric transformations, organizing statements and reasons systematically to prove geometric concepts and theorems accurately in geometric proofs.

3. Parallel and Perpendicular Lines

3.1 Parallel and Skew Lines - CCSS Standard: G-GPE.B.5
Analyze the characteristics and relationships of parallel and skew lines in three-dimensional space, understanding the properties of these lines and their intersection patterns to solve advanced problems related to parallel and skew lines in geometric figures.

3.2 Perpendicular Lines - CCSS Standard: G-GPE.B.5
Investigate perpendicular lines in three-dimensional shapes and space, applying the concepts of perpendicularity to analyze complex geometric structures and relationships between perpendicular lines in advanced geometric contexts.

3.3 Corresponding Angles - CCSS Standard: G-GPE.B.5
Identify and analyze corresponding angles in complex geometric configurations, exploring the properties and applications of corresponding angles in various geometric settings to solve intricate angle-related problems effectively.

3.4 Alternate Interior Angles - CCSS Standard: G-GPE.B.5
Recognize and analyze alternate interior angles in advanced geometric shapes, understanding the properties and relationships of these angles within complex geometric structures to solve challenging problems involving alternate interior angles.

3.5 Alternate Exterior Angles - CCSS Standard: G-GPE.B.5
Investigate and apply knowledge of alternate exterior angles in sophisticated geometric figures, analyzing the relationships and properties of alternate exterior angles within complex geometric configurations to solve advanced geometry problems effectively.

3.6 Same Side Interior Angles - CCSS Standard: G-GPE.B.5
Explore and understand same-side interior angles in intricate geometric shapes, analyzing the properties and relationships of these angles within complex geometric structures to solve challenging problems related to same-side interior angles.

3.7 Slope in the Coordinate Plane - CCSS Standard: G-GPE.B.5
Calculate and interpret the slope of a line in the coordinate plane in advanced geometric contexts, applying the concept of slope as a measure of steepness and rate of change to analyze complex linear relationships and solve sophisticated real-world problems.

3.8 Parallel Lines in the Coordinate Plane - CCSS Standard: G-GPE.B.5
Recognize and apply the concept of parallel lines in the coordinate plane in advanced geometric settings, understanding the properties of parallel lines and their implications in coordinate geometry to solve complex problems related to parallel lines.

3.9 Perpendicular Lines in the Coordinate Plane - CCSS Standard: G-GPE.B.5
Identify and apply the concept of perpendicular lines in the coordinate plane in advanced geometric contexts, understanding the relationship between perpendicular lines and their slopes to solve intricate geometry problems effectively.

3.10 Distance Formula in the Coordinate Plane - CCSS Standard: G-GPE.B.7
Utilize the distance formula to calculate distances between points in the coordinate plane in advanced geometric scenarios, applying the Pythagorean theorem and coordinate geometry techniques to determine distances accurately and solve complex problems.

3.11 Distance Between Parallel Lines - CCSS Standard: G-GPE.B.5
Calculate and analyze the distance between parallel lines in advanced geometric figures, applying geometric concepts and properties of parallel lines to determine distances accurately in complex geometric settings and real-world applications.

4. Triangles and Congruence

4.1 Triangle Sum Theorem - CCSS.MATH.CONTENT.HSG.CO.C.9
The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

4.2 Exterior Angles Theorems - CCSS.MATH.CONTENT.HSG.CO.C.11
The Exterior Angles Theorem states that an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

4.3 Congruent Triangles - CCSS.MATH.CONTENT.HSG.CO.C.8
Congruent Triangles have the same size and shape. When two triangles are congruent, all corresponding angles and sides are equal.

4.4 Congruence Statements - CCSS.MATH.CONTENT.HSG.CO.B.7
Congruence Statements are used to show that two figures are congruent by listing the congruent parts of the figures.

4.5 Third Angle Theorem - CCSS.MATH.CONTENT.HSG.CO.C.10
The Third Angle Theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

4.6 SSS Triangle Congruence - CCSS.MATH.CONTENT.HSG.CO.D.12
The Side-Side-Side (SSS) Congruence Postulate states that if three sides of one triangle are congruent to the three sides of another triangle, then the triangles are congruent.

4.7 SAS Triangle Congruence - CCSS.MATH.CONTENT.HSG.CO.D.13
The Side-Angle-Side (SAS) Congruence Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

4.8 ASA and AAS Triangle Congruence - CCSS.MATH.CONTENT.HSG.CO.D.14
The Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) Congruence Postulates state that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

4.9 HL Triangle Congruence - CCSS.MATH.CONTENT.HSG.CO.D.15
The Hypotenuse-Leg (HL) Congruence Postulate states that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

4.10 Isosceles Triangles - CCSS.MATH.CONTENT.HSG.CO.C.6
Isosceles Triangles have at least two congruent sides and two congruent angles.

4.11 Equilateral Triangles - CCSS.MATH.CONTENT.HSG.CO.C.7
Equilateral Triangles have three congruent sides and three congruent angles.

5. Triangle Relationships

5.1 Midsegment Theorem - CCSS.MATH.CONTENT.HSG.CO.C.9
The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half of its length.

5.2 Perpendicular Bisectors - CCSS.MATH.CONTENT.HSG.CO.C.11
Perpendicular Bisectors are lines or rays that intersect a segment at a right angle and divide it into two equal parts.

5.3 Angle Bisectors in Triangles - CCSS.MATH.CONTENT.HSG.CO.C.8
Angle Bisectors in Triangles are lines that divide an angle into two congruent angles, and the point of intersection is equidistant from the sides of the angle.

5.4 Medians - CCSS.MATH.CONTENT.HSG.CO.B.7
Medians of a triangle are segments from a vertex to the midpoint of the opposite side, and they intersect at the centroid, which divides each median into a 2:1 ratio.

5.5 Altitudes - CCSS.MATH.CONTENT.HSG.CO.C.10
Altitudes of a triangle are perpendicular segments from a vertex to the line containing the opposite side, and they can be inside, outside, or on the triangle.

5.6 Comparing Angles and Sides in Triangles - CCSS.MATH.CONTENT.HSG.CO.D.12
Comparing Angles and Sides in Triangles involves using properties like the Triangle Inequality Theorem and congruence postulates to compare and analyze relationships between angles and sides in triangles.

5.7 Triangle Inequality Theorem - CCSS.MATH.CONTENT.HSG.CO.D.13
The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

5.8 Indirect Proof in Algebra and Geometry - CCSS.MATH.CONTENT.HSG.CO.D.14
Indirect Proof in Algebra and Geometry involves proving a statement by assuming the opposite is true and arriving at a contradiction, thereby establishing the original statement's validity.

6. Polygons and Quadrilaterals

6.1 Interior Angles in Convex Polygons - CCSS.MATH.CONTENT.HSG.CO.C.9
This standard focuses on the relationship between the number of sides in a convex polygon and the sum of its interior angles, as represented by the formula ((n-2) \times 180^\circ).

6.2 Exterior Angles in Convex Polygons - CCSS.MATH.CONTENT.HSG.CO.C.9
CCSS.MATH.CONTENT.HSG.CO.C.9 addresses the relationship between the exterior angles of a convex polygon and the formula (360^\circ/n) for regular polygons.

6.3 Parallelograms - CCSS.MATH.CONTENT.HSG.CO.C.11
Properties related to opposite sides being parallel and opposite angles being congruent are explored under this standard when studying Parallelograms.

6.4 Quadrilaterals that are Parallelograms - CCSS.MATH.CONTENT.HSG.CO.C.8
Identifying and classifying quadrilaterals based on their properties, especially focusing on parallelograms, aligns with CCSS.MATH.CONTENT.HSG.CO.C.8.

6.5 Parallelogram Classification - CCSS.MATH.CONTENT.HSG.CO.C.10
In Parallelogram Classification, students differentiate between various types of parallelograms based on specific properties outlined in CCSS.MATH.CONTENT.HSG.CO.C.10.

6.6 Trapezoids - CCSS.MATH.CONTENT.HSG.CO.D.12
CCSS.MATH.CONTENT.HSG.CO.D.12 is relevant in exploring the characteristics of trapezoids, including understanding the bases, legs, and angles within the shape.

6.7 Kites - CCSS.MATH.CONTENT.HSG.CO.D.13
CCSS.MATH.CONTENT.HSG.CO.D.13 is applied to analyze the unique properties of kites, such as the presence of two distinct pairs of adjacent congruent sides.

6.8 Quadrilateral Classification - CCSS.MATH.CONTENT.HSG.CO.D.14
Focusing on the classification of quadrilaterals based on their properties, including parallelograms, rhombuses, rectangles, and squares, falls under the scope of CCSS.MATH.CONTENT.HSG.CO.D.14.

7. Similarity

7.1 Forms of Ratios - CCSS.MATH.CONTENT.HSG.CO.A.1
This standard involves understanding different forms of ratios, including part-to-part, part-to-whole, and whole-to-part, and applying them in various mathematical contexts.

7.2 Proportion Properties - CCSS.MATH.CONTENT.HSG.CO.A.2
focuses on the properties of proportions, such as the cross products property, and how to use them to solve proportion problems.

7.3 Similar Polygons and Scale Factors - CCSS.MATH.CONTENT.HSG.CO.A.4
Exploring similar polygons and scale factors involves understanding how corresponding angles are congruent and corresponding sides are in proportion, as outlined in.

7.4 AA Similarity - CCSS.MATH.CONTENT.HSG.SRT.A.2
The concept of Angle-Angle (AA) Similarity is covered under CCSS.MATH.CONTENT.HSG.SRT.A.2, where if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar.

7.5 Indirect Measurement - CCSS.MATH.CONTENT.HSG.SRT.A.3
Involves using proportional relationships to solve problems in real-world contexts, including indirect measurement where direct measurement is not feasible.

7.6 SSS Similarity - CCSS.MATH.CONTENT.HSG.SRT.B.4
CCSS.MATH.CONTENT.HSG.SRT.B.4 addresses Side-Side-Side (SSS) Similarity, stating that if the corresponding sides of two triangles are in proportion, the triangles are similar.

7.7 SAS Similarity - CCSS.MATH.CONTENT.HSG.SRT.B.4
Similarly, CCSS.MATH.CONTENT.HSG.SRT.B.4 covers Side-Angle-Side (SAS) Similarity, indicating that if two sides of a triangle are proportional to two sides of another triangle, and their included angles are congruent, the triangles are similar.

7.8 Triangle Proportionality - CCSS.MATH.CONTENT.HSG.SRT.B.6
Triangle Proportionality, as per CCSS.MATH.CONTENT.HSG.SRT.B.6, involves understanding the relationship between lines parallel to sides of a triangle and the resulting proportional segments they create.

7.9 Parallel Lines and Transversals - CCSS.MATH.CONTENT.HSG.CO.C.9
This standard includes the properties of parallel lines cut by a transversal, leading to relationships between angles such as corresponding, alternate interior, alternate exterior, and consecutive interior angles.

7.10 Proportions with Angle Bisectors - CCSS.MATH.CONTENT.HSG.CO.C.9
CCSS.MATH.CONTENT.HSG.CO.C.9 also covers the use of proportions involving angle bisectors in triangles, highlighting the relationships created by angle bisectors within similar triangles.

7.11 Dilation - CCSS.MATH.CONTENT.HSG.CO.A.3
The concept of dilation, encompassing the transformation of a figure by a scale factor around a center point, is addressed in CCSS.MATH.CONTENT.HSG.CO.A.3.

7.12 Dilation in the Coordinate Plane - CCSS.MATH.CONTENT.HSG.CO.A.2
Involving coordinate geometry, CCSS.MATH.CONTENT.HSG.CO.A.2 delves into dilations on the coordinate plane, emphasizing scale factors and the preservation of parallel lines.

7.13 Self-Similarity - CCSS.MATH.CONTENT.HSG.CO.A.4
Self-Similarity, an advanced topic related to figures that are similar to a part of themselves, is connected to CCSS.MATH.CONTENT.HSG.CO.A.4, focusing on the properties of self-similar shapes and their scale factors.

8. Right Triangle Trigonometry

8.1 Simplifying Radicals - CCSS.MATH.CONTENT.HSN.RN.A.2
This standard involves mastering the operations with radicals, especially simplifying expressions containing square roots and higher order roots, as outlined in CCSS.MATH.CONTENT.HSN.RN.A.2.

8.2 Pythagorean Theorem and Pythagorean Triples - CCSS.MATH.CONTENT.HSG.SRT.C.8
Involving the fundamental theorem in trigonometry, CCSS.MATH.CONTENT.HSG.SRT.C.8 covers the Pythagorean Theorem and Pythagorean triples, emphasizing the relationship between the sides of a right triangle.

8.3 Applications of the Pythagorean Theorem - CCSS.MATH.CONTENT.HSG.SRT.C.8
Real-world applications of the Pythagorean Theorem are explored under CCSS.MATH.CONTENT.HSG.SRT.C.8, focusing on its use in solving distance, area, and perimeter problems within geometric scenarios.

8.4 Inscribed Similar Triangles - CCSS.MATH.CONTENT.HSG.SRT.B.4
Understanding inscribed similar triangles involves recognizing the properties of triangles within circles and their connection to central angles, aligning with CCSS.MATH.CONTENT.HSG.SRT.B.4.

8.5 45-45-90 Right Triangles - CCSS.MATH.CONTENT.HSG.SRT.B.4
CCSS.MATH.CONTENT.HSG.SRT.B.4 also addresses the characteristics of 45-45-90 right triangles, focusing on the ratios between their sides and their relevance in geometric reasoning.

8.6 30-60-90 Right Triangles - CCSS.MATH.CONTENT.HSG.SRT.B.4
Similarly aligned with CCSS.MATH.CONTENT.HSG.SRT.B.4, the properties of 30-60-90 right triangles are studied, highlighting the proportions among their sides and their significance in trigonometry.

8.7 Sine, Cosine, Tangent - CCSS.MATH.CONTENT.HSG.SRT.C.8
The trigonometric ratios of sine, cosine, and tangent play a central role in CCSS.MATH.CONTENT.HSG.SRT.C.8, requiring a deep understanding of these ratios in right-angled triangles and their applications in trigonometry.

8.8 Trigonometric Ratios with a Calculator - CCSS.MATH.CONTENT.HSG.SRT.C.8
Utilizing calculators to compute trigonometric ratios is covered in CCSS.MATH.CONTENT.HSG.SRT.C.8, showcasing the integration of technology in trigonometry calculations and problem-solving.

8.9 Trigonometry Word Problems - CCSS.MATH.CONTENT.HSG.SRT.D.10
The application of trigonometric concepts to real-world scenarios is emphasized in Trigonometry Word Problems, aligning with CCSS.MATH.CONTENT.HSG.SRT.D.10, with a focus on solving problems related to angles of elevation and depression.

8.10 Inverse Trigonometric Ratios - CCSS.MATH.CONTENT.HSG.SRT.D.11
CCSS.MATH.CONTENT.HSG.SRT.D.11 delves into the concept of inverse trigonometric ratios, requiring students to understand and use functions like arcsine, arccosine, and arctangent to determine angles based on trigonometric values.

9. Circles

9.1 Parts of Circles - CCSS.MATH.CONTENT.HSG-C.A.1
This standard involves identifying and understanding the different components of circles, such as radius, diameter, circumference, and area, and how they interrelate within the circle's geometry, aligning with CCSS.MATH.CONTENT.HSG-C.A.1.

9.2 Tangent Lines - CCSS.MATH.CONTENT.HSG-C.A.4
CCSS.MATH.CONTENT.HSG-C.A.4 focuses on the properties and characteristics of tangent lines in circles, emphasizing their unique relationship with radii, perpendicularity, and the points of intersection with circles.

9.3 Arcs in Circles - CCSS.MATH.CONTENT.HSG-C.A.2
The measurement and properties of arcs within circles, including arc length, arc measures, central angles, and their association with the circle's circumference, are explored in CCSS.MATH.CONTENT.HSG-C.A.2.

9.4 Chords in Circles - CCSS.MATH.CONTENT.HSG-C.A.2
Understanding the properties and relationships of chords within circles, including their connection to corresponding arcs and their interactions within the circle's structure, is emphasized in CCSS.MATH.CONTENT.HSG-C.A.2.

9.5 Inscribed Angles in Circles - CCSS.MATH.CONTENT.HSG-C.A.2
CCSS.MATH.CONTENT.HSG-C.A.2 also covers inscribed angles within circles, examining the angles formed by chords, secants, and tangents, and their relationships with arc measures and circle properties.

9.6 Inscribed Quadrilaterals in Circles - CCSS.MATH.CONTENT.HSG-C.A.2
The characteristics and properties of inscribed quadrilaterals within circles, focusing on their angles and special properties in relation to circle arcs, are outlined in CCSS.MATH.CONTENT.HSG-C.A.2.

9.7 Angles On and Inside a Circle - CCSS.MATH.CONTENT.HSG-C.A.2
CCSS.MATH.CONTENT.HSG-C.A.2 addresses the angles formed within and on circles, including central angles, inscribed angles, and angles at the circumference, highlighting their geometric relationships and measurements.

9.8 Angles Outside a Circle - CCSS.MATH.CONTENT.HSG-C.A.2
The properties and characteristics of angles formed outside a circle, by lines intersecting the circle externally, are explored in CCSS.MATH.CONTENT.HSG-C.A.2, emphasizing their relationships with the circle's elements and angles inside the circle.

9.9 Segments from Chords - CCSS.MATH.CONTENT.HSG-C.A.4
This standard delves into the segments created by chords within circles, focusing on their properties, lengths, and relationships with the chords and the circle's center, as per CCSS.MATH.CONTENT.HSG-C.A.4.

9.10 Segments from Secants - CCSS.MATH.CONTENT.HSG-C.A.4
CCSS.MATH.CONTENT.HSG-C.A.4 also covers segments generated by secants intersecting circles, emphasizing their properties, lengths, and relationships with circle elements and angles within the circle.

9.11 Segments from Secants and Tangents - CCSS.MATH.CONTENT.HSG-C.A.4
Exploring segments formed by secants and tangents in circles, CCSS.MATH.CONTENT.HSG-C.A.4 involves understanding their lengths, relationships with each other, and connections to circle properties and angles.

9.12 Circles in the Coordinate Plane - CCSS.MATH.CONTENT.HSG-GPE.A.1
CCSS.MATH.CONTENT.HSG-GPE.A.1 focuses on representing circles within the coordinate plane, analyzing circle equations, properties, and graphing circles using coordinate geometry techniques for tenth-grade mathematics.

10. Perimeter and Area

10.1 Area and Perimeter of Rectangles - G-MG.A.1
Students will calculate the area and perimeter of rectangles, applying the formulas and concepts related to these geometric properties.

10.2 Area of a Parallelogram - G-MG.A.2
This standard focuses on finding the area of parallelograms by applying the appropriate formula and understanding the geometric properties of parallelograms.

10.3 Area and Perimeter of Triangles - G-MG.A.1
Students will determine the area and perimeter of triangles, utilizing the respective formulas and properties associated with triangles.

10.4 Area of Composite Shapes - G-MG.A.3
Understanding how to calculate the area of composite shapes by decomposing them into simpler shapes and summing their areas.

10.5 Area and Perimeter of Trapezoids - G-MG.A.1
Calculating the area and perimeter of trapezoids involves applying the formulas specific to trapezoids and understanding their geometric properties.

10.6 Area and Perimeter of Rhombuses and Kites - G-MG.A.1
Students will determine the area and perimeter of rhombuses and kites, applying the formulas for these two types of quadrilaterals.

10.7 Area and Perimeter of Similar Polygons - G-SRT.A.2
Understanding the relationship between area and perimeter of similar polygons, including how scaling impacts these properties.

10.8 Circumference - G-GMD.A.1
This standard focuses on calculating the circumference of circles, emphasizing the use of the formula involving pi and the circle's diameter or radius.

10.9 Arc Length - G-C.A.2
Students will calculate the arc length of circles by applying the central angle and the circle's radius to find the fraction of the circumference.

10.10 Area of a Circle - G-C.A.1
Understanding and applying the formula for finding the area of a circle using its radius or diameter and the constant pi.

10.11 Area of Sectors and Segments - G-C.A.2
Calculating the area of sectors and segments of circles involves understanding the fractional part of the circle they represent and applying the corresponding formulas.

11. Surface Area and Volume

11.1 Polyhedrons - G-GMD.A.1
Students will explore the characteristics and properties of polyhedrons, including vertices, edges, and faces, to classify and analyze different types of polyhedra.

11.2 Cross-Sections and Nets - G-GMD.A.3
Understanding how to create cross-sections of three-dimensional figures and represent them as nets, aiding in visualizing and understanding the structure of solids.

11.3 Prisms - G-GMD.A.2
This standard focuses on prisms, their properties, such as the number of faces, edges, and vertices, as well as calculating the volume and surface area of prisms.

11.4 Cylinders - G-GMD.A.3
Students will learn about cylinders, including their properties and how to calculate their volume and surface area, enhancing their understanding of three-dimensional shapes.

11.5 Pyramids - G-GMD.A.3
Understanding the characteristics of pyramids, including the number of faces, edges, and vertices, and how to calculate their volume and surface area based on their geometric properties.

11.6 Cones - G-GMD.A.3
This standard focuses on cones, their properties, such as the slant height, base radius, and height, and how to calculate their volume and surface area using specific formulas.

11.7 Spheres - G-GMD.A.4
Students will explore the properties of spheres, such as radius and diameter, and learn to calculate their volume and surface area, deepening their understanding of three-dimensional shapes.

11.8 Composite Solids - G-GMD.A.3
Understanding composite solids involves analyzing and calculating the volume and surface area of complex three-dimensional figures made up of simpler shapes like prisms, pyramids, cylinders, and cones.

11.9 Area and Volume of Similar Solids - G-SRT.C.8
Students will explore the relationship between the areas and volumes of similar solids, understanding how scaling affects these properties and applying proportional reasoning to solve problems related to similar solids.

12. Rigid Transformations

12.1 Reflection Symmetry - G-CO.A.3
Students will explore reflection symmetry, understanding how to identify and create reflections across a line of symmetry, leading to a deeper comprehension of geometric transformations.

12.2 Rotation Symmetry - G-CO.A.2
This standard focuses on rotation symmetry, where students will learn about rotational transformations and identify figures that exhibit rotational symmetry, enhancing their understanding of geometric concepts.

12.3 Geometric Translations - G-CO.A.4
Understanding geometric translations involves students learning how to translate or slide figures in a coordinate plane, applying the concepts of vectors and ordered pairs to describe these transformations.

12.4 Rotations - G-CO.A.3
Students will explore rotations as geometric transformations, understanding how figures can be rotated around a point and identifying rotational properties of shapes.

12.5 Reflections - G-CO.A.3
This standard focuses on reflections as transformations, where students will learn to reflect figures over a line, axis, or another figure, deepening their understanding of symmetry and transformations.

12.6 Composition of Transformations - G-CO.A.3
Understanding the composition of transformations involves combining multiple transformations like reflections, rotations, and translations to manipulate figures, leading to a more comprehensive understanding of geometric transformations.

12.7 Tessellations - G-CO.B.6
Students will explore tessellations, understanding how shapes can be repeated to cover a plane without any gaps or overlaps, leading to the creation of artistic and mathematically interesting patterns.

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