Geometry

Quarterly Overview of Geometry

The objectives and outcomes for each unit are common across FCPS and based on the Virginia Standards of Learning. The pacing by quarter and by week provides an example of how the curriculum can be organized throughout the year. Teacher teams may adjust the pacing or order of units to best meet the needs of students.

Week 1Week 2Week 3 Week 4Week 5Week 6 Week 7Week 8Week 9

Units and Details

Unit 1: Geometry Basics

Students will:

• Determine the coordinates of the midpoint or endpoint of a segment, using the midpoint formula.
• Use a formula to determine the slope of a line.
• Apply the distance formula to determine the length of a line segment when given the coordinates of the endpoints.
• Construct and justify the constructions of a line segment congruent to a given line segment, the perpendicular bisector of a line segment, the bisector of a given angle, and an angle congruent to a given angle.

Unit 2: Logic and Reasoning

Students will:

• Identify the converse, inverse, and contrapositive of a conditional statement.
• Translate verbal arguments into symbolic form using the symbols of formal logic.
• Determine the validity of a logical argument using valid forms of deductive reasoning.
• Determine that an argument is false using a counterexample.
• Evaluate the truth value of simple and compound statements. (Honors)

Unit 3: Parallel and Perpendicular Lines

Students will:

• Solve problems by using the relationships between pairs of angles formed by the intersection of two parallel lines and a transversal including corresponding angles, alternate interior angles, alternate exterior angles, same-side (consecutive) interior angles, and same-side (consecutive) exterior angles.
• Solve problems, including practical problems, involving intersecting and parallel lines.
• Compare the slopes to determine whether two lines are parallel, perpendicular, or neither.
• Prove two or more lines are parallel given angle measurements expressed numerically or algebraically.
• Prove two lines are parallel using deductive proofs given relationships between and among angles.
• Construct and justify the constructions of a perpendicular to a given line from a point not on the line, a perpendicular to a given line at a given point on the line, and a line parallel to a given line through a point not on the line.

Unit 4: Properties of Triangles

Students will:

• Given information about the lengths of sides and/or measures of angles in triangles, solve problems, including practical problems.
• Order the sides of a triangle by their lengths when given information about the measures of the angles and order the angles given side lengths.
• Given the lengths of three segments, determine whether a triangle could be formed.
• Given the lengths of two sides of a triangle, determine the range in which the length of the third side must lie.
• Construct and justify the constructions of an equilateral triangle.
• Investigate and construct the points of concurrency. (Honors)
• Determine the midsegments and use related properties. (Honors)

Unit 5: Triangles and Triangle Congruence

Students will:

• Prove two triangles congruent given relationships among angles and sides of triangles expressed numerically or algebraically.
• Prove two triangles congruent given representations in the coordinate plane and using coordinate methods (distance formula and slope formula).
• Use direct proofs to prove two triangles congruent.

Unit 6: Similar Triangles

Students will:

• Prove two triangles similar given relationships among angles and sides of triangles expressed numerically or algebraically.
• Prove two triangles similar given representations in the coordinate plane and using coordinate methods (distance formula and slope formula).
• Use direct proofs to prove triangles similar.

Unit 7: Right Triangles

Students will:

• Solve problems, including practical problems, using right triangle trigonometry and properties of special right triangles.
• Determine whether a triangle formed with three given lengths is a right triangle.
• Solve for missing lengths in geometric figures, using properties of 30°-60°-90° and 45°-45°-90° triangles where rationalizing denominators may be necessary.
• Solve problems, including practical problems, involving right triangles with missing side lengths or angle measurements, using sine, cosine, and tangent ratios.

Unit 8: Polygons

Students will:

• Solve problems, including practical problems, using the properties specific to parallelograms, rectangles, rhombi, squares, isosceles trapezoids, and trapezoids.
• Prove that quadrilaterals have specific properties, using coordinate and algebraic methods, such as the distance formula, slope, and midpoint formula.
• Prove the properties of quadrilaterals, using direct proofs.
• Solve problems, including practical problems, involving angles of convex polygons.
• Determine the sum of the measures of the interior and exterior angles of a convex polygon and the measure of each interior and exterior angle of a regular polygon.
• Determine the number of sides of a regular polygon, given the measures of interior or exterior angles of the polygon.
• Construct and justify the constructions of an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
• Find the area and perimeter of a regular polygon, given the length of one side or the radius of the polygon. (Honors)

Unit 9: Circles

Students will:

• Solve problems, including practical problems, by applying properties of circles.
• Determine angle measures formed by intersecting chords, secants, and/or tangents.
• Determine lengths of segments formed by intersecting chords, secants, and/or tangents.
• Calculate the length of an arc of a circle.
• Calculate the area of a sector.
• Solve problems involving equations of circles.
• The student will construct and justify the constructions of the inscribed and circumscribed circles of a triangle and a tangent line from a point outside of a given circle to the circle. (Honors)

Unit 10: Solids

Students will:

• Solve problems including practical problems, involving surface area and volume of cylinders, prisms, pyramids, cones, hemispheres, and spheres, using appropriate formulas. This includes composite three-dimensional figures.
• Solve problems, including practical problems, involving the lateral area of circular cylinders, prisms, and regular pyramids.
• Given information about a three-dimensional figure such as length of a side, area of a face, or volume, determine missing information.
• Compare ratios between side lengths, perimeters, areas, and volumes, given two similar figures.
• Describe how changes in one or more dimensions affect other derived measures (perimeter, area, surface area, and volume) of a figure.
• Solve real-world problems involving measured attributes of similar figures.

Unit 11: Transformations

Students will:

• Determine whether a figure has point symmetry, line symmetry, both, or neither.
• Given an image and preimage, identify the transformation or combination of transformations that has/have occurred. Transformations include: a translation,  a reflection (over any horizontal or vertical line or the lines y = x or y = −x), a clockwise or counterclockwise rotation (of 90°, 180°, 270°, or 360° on a coordinate grid where the center of rotation is limited to the origin), and a dilation (from a fixed point on a coordinate grid).
• Investigate vectors and their applications. (Honors)

SOL Review, Remediation, and Post SOL Activities

Students will:

• Make connections between big ideas learned throughout the course.
• Deepen and extend skills learned during the course.

Assessments

Student assessments are part of the teaching and learning process.

• Teachers give assessments to students on an ongoing basis to
• Check for understanding
• Gather information about students' knowledge or skills.
• Assessments provide information about a child's development of knowledge and skills that can help families and teachers better plan for the next steps in instruction.

For testing questions or additional information about how schools and teachers use test results to support student success, families can contact their children's schools.

In Fairfax County Public Schools (FCPS), tests focus on measuring content knowledge and skill development.