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.

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)

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.

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)

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.

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.

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.

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)

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)

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.

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)

Students will:

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