Honors 1 Geometry

Scope and Sequence

NCTM Standards covered in this course:

  • Compute fluently and make reasonable estimates
  • Understand patterns, relations, and functions
  • Use mathematical models to represent and understand quantitative relationships
  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems
  • Use visualization, spatial reasoning, and geometric modeling to solve problems
  • Understand measurable attributes of objects and the units, systems, and processes of measurement
  • Apply appropriate techniques, tools, and formulas to determine measurements
  • Problem solving, reasoning and proof, communication, connections, and representations are also addressed in this course.

KentuckyState Standards covered in this course:

  • Problem solving
  • Mathematical communication
  • Mathematical connections
  • Mathematical reasoning
  • Proportional reasoning
  • General relationships
  • Relationships in triangles
  • Quadrilateral relationships
  • Other polygons and circles
  • Congruence and similarity
  • Measurements
  • Coordinate geometry and transformations

Tools of Geometry – 8 days

1. Points, Lines and Planes

2. Measuring Segments

3. Measuring Angles

4. Exploring Angle Pairs

5. Midpoint and Distance in the Coordinate Plane

6. Perimeter, Circumference, and Area

Reasoning and Proof – 6 days

1. Patterns and Inductive Reasoning

2. Conditional Statements

3. Biconditionals and Definitions

4. Deductive Reasoning

5. Reasoning in Algebra and Geometry

6. Proving Angles Congruent

Parallel and Perpendicular Lines – 7 days

1.Lines and Angles

2.Properties of Parallel Lines

3.Proving Lines Parallel

4.Parallel and Perpendicular Lines

5.Parallel Lines and Triangles

Congruent Triangles – 8 days

  1. Congruent Figures
  2. Triangle Congruence by SSS and SAS
  3. Triangle Congruence by ASA and AAS
  4. Using Corresponding Parts of Congruent Triangles
  5. Isosceles and Equilateral Triangles
  6. Congruence in Overlapping Triangles

Relationships in Triangles – 3 days

  1. Midsegments of Triangles
  2. Perpendicular and Angle Bisectors
  3. Bisectors in Triangles
  4. Medians and Altitudes
  5. Inequalities in Triangles

Polygons and Quadrilaterals – 7 days

  1. The Polygon-Angle Sum Theorems
  2. Properties of Parallelograms
  3. Proving that a Quadrilateral is a Parallelogram
  4. Properties of Rhombuses, Rectangles, and Squares
  5. Conditions for Rhombuses, Rectangles, and Squares
  6. Trapezoids and Kites

Similarity – 7 days

  1. Ratios and Proportions
  2. Similar Polygons
  3. Proving Triangles Similar
  4. Similarity in Right Triangles
  5. Proportions in Triangles

Right Triangles and Trigonometry – 7 days

  1. The Pythagorean Theorem and Its Converse
  2. Special Right Triangles
  3. Trigonometry
  4. Angles of Elevation and Depression

Circles – 6 days

  1. Tangent Lines
  2. Chords and Arcs
  3. Inscribed Angles
  4. Angles Measures and Segment Lengths

Areas– 6 days

  1. Areas of Parallelograms and Triangles
  2. Areas of Trapezoids, Rhombuses, and Kites
  3. Areas of Regular Polygons
  4. Trigonometry and Area
  5. Circles and Arcs
  6. Areas of Circles and Sectors
  7. Geometry Probability

Surface Area – 4 days

  1. Surface Areas of Prisms and Cylinders
  2. Surface Areas of Pyramids and Cones
  3. Surface Areas Spheres

Volume – 4 days

1. Volumes of Prisms and Cylinders

2. Volumes of Pyramids and Cones

3. Volumes of Spheres

Outcomes for Honors 1 Geometry

  1. Students will exhibit knowledge of and be able to explain the relationships between basic geometric terms and key postulates.
  2. Students will solve multiple step geometry problems that involve integrating concepts, planning, visualization and making connections with other content areas.
  3. Students will analyze angles associated with parallel lines and their properties.
  4. Students will identify and classify triangles by various methods.
  5. Students will test for and prove triangle congruence.
  6. Students will apply their knowledge of ratio and proportion to geometric figures.
  7. Students will apply the Pythagorean Theorem.
  8. Students will apply properties of special right triangles and will use trigonometry to solve problems dealing with these special right triangles.
  9. Students will learn and apply the properties of quadrilaterals.
  10. Students will learn parts of circle, and will be able to measure angles and arcs of circles.
  11. Students will be able to find perimeter, area and volume of geometric figures.
  12. Students will be able to apply concepts of geometry to everyday life.

Revised August 2017