Fairview High School
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Geometry Honors
Essential Outcomes
Fairview High School

Geometry Honors A

Points, Lines, Planes, and Angles

  • Identify and model points, lines, and planes.

  • Identify collinear and coplanar points and intersecting lines and planes in space.

  • Measure and compute with measures to determine accuracy.

  • Find the distance and midpoint between two points.

  • Measure and classify angles using constructions.

  • Use the constructions to identify congruent angles and their bisectors.

  • Use constructions to find segment bisectors, perpendicular bisectors, congruent angles, and segment trisectors.

  • Identify special pairs of angles such as vertical, adjacent, and perpendicular.

  • Identify, name, and find the perimeters of polygons.

Reasoning and Proof

  • Make conjectures based on inductive reasoning and using counterexamples to disprove these conjectures.

  • Determine the truth values of conjunctions and disjunctions using truth tables.

  • Analyze statements in if-then statements.

  • Write the converse, inverse, and contrapositive of if-then form.

  • Use the Law of Detachment and the Law of Syllogism.

  • Use algebra to write two-column proof.

  • Use properties of equality in geometry proofs.

  • Write proofs involving segment addition and congruence.

  • Write proofs involving supplementary and complementary angles.

  • Write proofs involving congruent and right angles.

Parallel and Perpendicular Lines

  • Identify the relationships between two lines or two planes and name the angles formed by the parallel lines and transversal.

  • Use the properties of parallel line to determine congruent angles and solve the measures by using algebra.

  • Finding slope to determine parallel and perpendicular lines.

  • Write an equation of a line given information about the graph.

  • Solve problems by writing equations.

  • Recognize angle conditions that occur with parallel lines.

  • Prove the two lines are parallel based on given angle relationships.

  • Find the distance between parallel lines and a point and a line.

Congruent Triangles

  • Identify and classify triangles by angles and sides.

  • Apply the Angle Sum Theorem and the Exterior Angle Theorem.

  • Name and label corresponding parts of congruent triangles.

  • Identify congruence transformations.

  • Use the SSS, SAS, ASA, and AAS postulates to prove triangle congruent.

  • Use properties of isosceles and equilateral triangles.

  • Position and label triangles for use in coordinate proofs.

Relationships in Triangles

  • Identify and use perpendicular bisector, angle bisectors, medians, and altitudes in triangles.

  • Recognize and apply properties of inequalities to the measure of angles of a triangle and between angles and the sides of a triangle.

  • Apply the Triangle Inequality Theorem.

  • Determine the shortest distance between a point and a line.

  • Apply the SAS and SSS inequality.

Proportions and Similarity

  • Write ratios and use properties of proportions.

  • Identify similar figures.

  • Solve problems involving scale factors.

  • Identify similar triangles.

  • Use similar triangles to solve problems.

  • Use proportional parts of triangles.

  • Recognize and use proportional relationships of corresponding perimeters of similar triangles.

  • Recognize and use proportional relationships of corresponding angle bisectors, altitudes, and medians of similar triangles.

  • Discover the use of fractals and iteration in nature and in the project "Sierpenski's Tetrahedron".

Geometry Honors B

Right Triangles and Trigonometry

  • Find the geometric mean between two numbers.

  • Solve problems involving relationships between parts of right triangles and the altitude to its hypotenuse.

  • Use the Pythagorean Theorem and its converse.

  • Use properties of the 45-45-90 and the 30-30-30 triangles.

  • Find trigonometric ratios using right triangles and solving problems using these ratios.

  • Solve problems using angles of depression and elevation.

  • Use the Law of Sines to solve triangles and problems using the Law of Sines.

  • Use the Law of Cosines to solve triangles and problems using the Law of Cosines.

Quadrilaterals

  • Find the sum of the interior and exterior angles of a polygon.

  • Recognize and apply properties of the sides, angles, and diagonals of parallelograms.

  • Recognize the conditions that ensure quadrilateral is a parallelogram.

  • Prove that a set of points forms a parallelogram in the coordinate plane.

  • Apply properties of rectangles.

  • Determine whether parallelograms are rectangles.

  • Recognize and apply properties of rhombi and squares.

  • Recognize and apply properties of trapezoids.

  • Solve problems involving the medians of trapezoids.

Transformations

  • Draw reflected images.

  • Recognize and draw lines of symmetry and points of symmetry.

  • Draw translated images using coordinates.

  • Draw translated images by using repeated reflections.

  • Draw rotated images using the angle of rotation.

  • Identify figures with rotational symmetry.

  • Identify regular tessellations and create tessellations with specific attributes.

  • Determine whether a dilation is an enlargement, a reduction, or a congruence transformation.

  • Determine the scale factor for a given dilation.

  • Find magnitudes and directions of vectors.

  • Perform translations with vectors.

Circles

  • Identify and use parts of a circle and solve problems involving the circumference of a circle.

  • Recognize major arcs, minor arcs, semicircles, and central angles and their measure and finding arc length.

  • Recognize and use relationships between arcs, chords, and diameters.

  • Find measures of inscribed angles.

  • Find measures of angles of inscribed polygons.

  • Use properties of tangents and solve problems involving circumscribed polygons.

  • Find measures of angles formed by lines intersecting on, in, or on the outside of a circle.

  • Find the measure of segments that intersection the interior and the exterior of a circle.

  • Write an equation of a circle and graph it on a coordinate plane.

Areas of Polygons and Circles

  • Find the perimeters and area of parallelograms.

  • Find the area of triangles, trapezoids, and rhombi.

  • Fine the areas of regular polygons and circles.

  • Find the areas of irregular figures on a coordinate plane.

  • Solve problems involving geometric probability, sectors, and segments of circles.

Surface Area and Volume

  • Find the lateral area, surface area, and volume of prisms.

  • Find the lateral area, surface area, and volume of cylinders.

  • Find the lateral area, surface area, and volume of pyramids.

  • Find the lateral area, surface area, and volume of cones.

  • Find the lateral area, surface area, and volume of spheres.

 

 

 

 

2595 Fairview Blvd.
Fairview, TN 37062
Phone: 615-472-4400   Fax: 615-472-4421

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