Fairview High School
Inventing Quality Work For Students

Geometry
Essential Outcomes
Fairview High School

Geometry A

Reasoning and Proofs

• Use inductive reasoning to make conjectures.

• Understand basic terms and postulates or geometry.

• Recognize conditional statements.

• Write the converses of conditional statements.

• Write biconditional statements.

• Recognize good definitions.

• Use the Law of Detachment.

• Use the Law of Syllogism.

• Connect reasoning in algebra and geometry.

• Write a negation of a statement and the inverse of a contra positive of a conditional statement.

• Use direct reasoning.

• Use segments and area models to find the probabilities of events.

• Write ratios and solve proportions.

Lines, Segments, and Angles

• Identify segments and rays.

• Recognize parallel lines.

• Find lengths of segments.

• Find the measure of angles.

• Use a compass and straightedge to construct congruent segments and angles.

• Use a compass and straightedge to bisect segments and angles.

• Find the distance between two points.

• Find the coordinates of midpoint.

• Graph lines given their equations.

• Write equations of lines.

Perpendicular and Parallel Lines

• Identify angles pairs.

• Prove and apply theorems about angles.

• Identify angles formed by two lines and a transversal.

• Prove and use properties of parallel lines.

• Use a transversal to prove lines parallel.

• Relate parallel and perpendicular lines.

• Relate slope and parallel lines.

• Relate slope and perpendicular lines.

• Construct parallel lines.

• Construct perpendicular lines.

Triangles

• Classify triangles and find the measure of their angles.

• Use exterior angles of triangles.

• Show triangles are congruent using SSS and SAS.

• Show triangles are congruent using ASA and AAS.

• Show corresponding parts of congruent triangles are congruent.

• Use properties of isosceles and equilateral triangles.

• Use the HL Congruence Theorem and summarize congruence postulate and theorems.

• Identify congruent overlapping triangles.

• Prove two triangles are congruent by first proving two other triangles congruent.

• Use properties of midsegments to solve problems.

• Use properties of perpendicular and angle bisectors in triangles.

• Identify properties of median and altitudes in triangles.

• Use inequalities involving angles and sides of triangles.

• Find the area of triangles.

• Use the Pythagorean Theorem and its converse.

• Find the side lengths of 45-45-90 triangles.

• Find the side lengths of 30-60-90 triangles.

• Show that two triangles are similar using AA Similarity Postulates.

• Show that two triangles are similar using SSS and SAS Similarity Theorems.

• Find and use relationships in similar right triangles.

• Use the Side Splitter theorem.

• Use the Triangle-Angle-Bisector theorem.

Right Triangles

• Use tangent ratios to determine side lengths in triangles.

• Use sine and cosine to determine side lengths in triangles.

• Use angles of elevation and depression to solve problems.

• Describe vectors.

• Solve problems involving vector addition.

• Find the area of a triangle using trigonometry.

Polygons

• Create polygons.

• Find the sum of the measures of the interior and exterior angles of polygons.

• Recognize congruent figures and their corresponding parts.

• Identify and classify polygons-find angle measures of quadrilaterals.

• Use relationships involving diagonals of parallelograms or transversals.

• Determine whether a quadrilateral is a parallelogram.

• Use properties of diagonals of rhombuses and rectangles.

• Determine whether a quadrilateral is a rhombus or rectangle.

• Verify and use properties of trapezoids and kites.

• Name coordinates of special figures by using their properties.

• Prove theorems using figures in a coordinate plane.

• Find the area of parallelograms.

• Find the area of trapezoids.

• Find the area of a rhombus or kite.

• Find the area of a regular polygon.

• Find the perimeters and areas of similar figures.

• Find the area of a regular polygon suing trigonometry.

Circles

• Find the measures of central angles and arcs.

• Find the circumference and arc length.

• Find areas of circles, sectors, and segments of circles.

• Use relationships between radius and tangent.

• Use the relationship between two tangents from one point.

• Use congruent arcs, chords, and central angles.

• Recognize properties of lines through the center of a circle.

• Find the measure of inscribed angles.

• Find the measure of an angle formed by chords, secants, and tangents.

• Find the lengths of segments associated with circles.

• Write the equation of a circle.

• Find the center and radius of a circle.

• Draw and describe a locus.

Three Dimensional Figures

• Recognize nets of space figures.

• Make isometric and orthographic drawings.

• Describe cross sections of three dimensional drawings.

• Find the surface area of cylinders and prisms.

• Find the surface area of pyramids and cones.

• Find the volumes of prisms and cylinders.

• Find the volumes of pyramids and cones.

• Find the areas and volumes of spheres.

• Find the relationships between ratios of the areas and volumes of similar solids.

Transformations

• Identify isometrics.

• Find reflection images of figures.

• Describe translations using vectors.

• Find translation images using matrix and vector sums.

• Draw and identify rotation images and figures.

• Use compositions of reflections.

• Identify glide reflections.

• Identify the type of symmetry in a figure.

• Identify transformations in tessellations and figures that will tessellate.

• Identify symmetries in tessellations.

• Locate dilation images of figures.

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Fairview, TN 37062
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