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HONORS Geometry Unit 1 Basics of Geometry (3 weeks) Topic Geometry Content Skills Assessments Standards A. History A.1 A.2 A.3 A.4 A.5 Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.1 1.2 1.4 1.5 1.7 1.8 1.9 1.10 2.1 2.2 2.3 2.4 2.5 3.1 3.2 4.1 4.2 5.1 5.2 6.1 6.2 B. Review of Coordinate Geometry Name 3 historical origins of geometry Name modern uses of geometry Name important contributions of Euclid Name important contributions of Descartes Name important contributions of Pythagoras C. Inductive Reasoning D. Structure of Mathematical System B.1 Plot a point B.2 Identify coordinates of a plotted point B.3 Calculate distance B.4 Measure the length of a segment B.5 Calculate midpoint B.6 Construct midpoint B.7 Construct an angle and angle bisector B.8 Calculate the measure of an angle using angles pairs (vertical, linear pair, complements, supplements) B.9 Classify angles (acute, right, obtuse, straight) B.10 Calculate perimeter and area of basic shapes (triangles, rectangles, circles) C.1 Define inductive logic and counterexample C.2 Formulate a conjecture C.3 Apply a definition C.4 Formulate a definition C.5 Predict a pattern D.1 Define postulate D.2 Define theorem D.3 Define and identify assumption D.4 Explain and illustrate geometric terms (defined and undefined) HONORS Geometry Unit # 2 Logic (3 weeks) Topic Geometry Content Skills Assessments Standards A. Reasoning A.1Define and identify a hypothesis A.2 Define and identify a conclusion A.3 Identify, write, and analyze conditional statements A.4 Identify and write converses A.5 Identify and write negations A.6 Identify and write inverses A.7 Identify and write contrapositives A.8 Identify and write biconditional statements A.9 Identify equivalent statements Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.1 1.2 1.3 1.4 1.5 1.6 1.8 1.10 2.3 B. Arguments C. Constructions D. Truth Tables B.1 Define and identify logical argument B.2 Construct a logical argument B.3 Judge the validity of a logical argument B.4 Draw conclusions using logical reasoning B.5 Define and identify deductive reasoning B.6 Draw conclusions using deductive reasoning with definitions B.7 Use symbolic notation to represent an argument B.8 Apply detachment and syllogism to an argument B.9 Apply algebraic properties to solve an equation B.10 Write a two-column proof for equations B.11 Write a two-column proof for special angles and segments B.12 Justify segment an angle congruence using properties B.13 Apply postulates to problem solving C.1 Copy an angle C.2 Copy a segment D.1 Apply basic rules of logic using truth tables to determine the validity of a statement HONORS Geometry Unit # 3 Parallel and Perpendicular Lines (3 weeks) Topic Geometry Content A. Parallel B. Perpendicular C. Arguments D. Slope Skills A.1 Define and identify parallel lines and skew lines A.2 Compare perpendicular, parallel and skew lines A.3 Compare parallel lines to parallel planes A.4 Construct parallel lines A.5 Define and identify a transversal A.6 Identify special angle pairs formed by parallel lines and a transversal A.7 Prove lines are parallel using special angle theorems A.8 Calculate measures of special angles on parallel lines A.9 Create proofs using converses of the parallel postulate and theorems A.10 Construct perspective drawings to represent parallel lines realistically A.11 Solve real-life problems using parallel lines A.12 Represent parallel lines in 3-dimensional space B.1 Define and identify perpendicular lines B.2 Compare perpendicular lines and skew lines B.3 Calculate measures of angles formed by perpendicular lines B.4 Create proofs using perpendicular theorems B.5 Construct perpendicular lines C.1 Create a flow proof C.2 Create a paragraph proof C.3 Create a two-coumn proof D.1 Define and calculate slope D.2 Identify the y-intercept of a line D.3 Use slopes to identify parallel and perpendicular lines D.4 Write the equation of a line using slope and yintercept, using two points, and from a graph D.5 Identify an write the equations of parallel and perpendicular lines Assessments Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) Standards 1.1 1.2 1.6 1.8 1.9 1.10 2.2 2.3 2.5 HONORS Geometry Unit # 4 Congruent Triangles (3 weeks) Topic Geometry Content Skills Assessments Standards A. Terminology A.1 Define triangle and related terms A.2 Classify triangles by sides A.3 Classify triangles by angles Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.10 3.4 3.5 3.6 3.7 3.8 3.9 3.10 B. Triangle Relationships C. Triangle Congruence D. Special Triangle Congruences B.1 Apply triangles inequality B.2 Find the possible lengths of the third side of a triangle B.3 Calculate the third angle of a triangle B.4 Find interior and exterior angles of a triangle using the exterior angles theorem B.5 Find the measures of the angles and sides of a right triangle C.1 Indentify and prove triangles are congruent by corresponding parts C.2 Apply the Third Angle Theorem C.3 Explain properties of congruent triangles (Reflexive, Symmetric, & Transitive) C.4 Prove triangles are congruent by postulates and theorems C.5 Construct congruent triangles using congruence postulates and theorems C.6 Complete a coordinate proof of congruent triangles D.1 Apply Base Angles Theorem and its converse D.2 Apply equilateral/Equiangular corollary and its converse HONORS Geometry Unit # 5 Properties of Triangles (3 weeks) Topic Geometry Content Perpendicular Bisectors B. Angle Bisectors C. Points of Concurrency D. Segments of triangles D.1 Midsegments D.2 Triangle Inequality D.3 Hinge Theorem Skills A.1 Define and identify a perpendicular bisector A.2 Calculate angle measures and segment lengths using a perpendicular bisector A.3 Complete proofs using perpendicular bisectors A.4 Construct a perpendicular bisector with straight edge and compass B.1 Define and identify an angle bisector B.2 Calculate angle measures and segment lengths using angle bisectors B.3 Complete proofs using angle bisectors B.4 Construct an angle bisector using straight edge and compass E. Indirect Proof C.1 Identify, locate, and define points of concurrency C.2 Calculate segment lengths using right triangles and congruent triangles determined by points of concurrency C.3 Solve for segment lengths using circles determined by circumcircle and incircle C.4 Construct all four points of concurrency with geometry software D.1 Construct the midsegment of a triangle D.2 Calculate segment lengths using the midsegment theorem D.3 Complete proofs using the midsegment theorem. D.4 Calculate side lengths of triangles using the triangle inequality theorem D.5 Order the angle measures and side lengths of a triangle by size D.6 Compare side lengths and angle measures using the Hinge theorem and its converse E.1 Complete an indirect proof Assessments Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) Standards 1.1 1.4 1.6 1.9 1.10 2.2 2.5 3.5 3.10 6.1 6.2 HONORS Geometry Unit # 6 Quadrilaterals (3 weeks) Topic Geometry Content Skills Assessments Standards A. Polygons A.1 Define, name, and identify polygons in terms of number of sides, convex/concave, equilateral/equiangular/regular Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.1 1.3 1.10 2.1 2.2 2.3 2.4 2.5 3.2 3.10 4.1 4.2 4.3 4.5 6.1 6.2 B. Parallelograms C. Other Quadrilaterals D. Areas A.2 Calculate the number of degrees in a convex polygon. A.3 Calculate the number of diagonals in a convex polygon. B.1 List and apply the 5 properties of a parallelogram to calculate segment lengths and angle measures B.2 List and apply 6 ways to prove a quadrilateral is a parallelogram. C.1 Identify and define special quadrilaterals, including rectangle, rhombus, square, trapezoid, isosceles trapezoids and kites. C.2 Calculate angle measures and segment lengths from properties of special quadrilaterals C.3 Prove a quadrilateral is a special type using twocolumn proof and coordinate geometry proof. C.4 Calculate the areas of special quadrilaterals and composite figures HONORS Geometry Unit # 7 Transformations (3 weeks) Topic Geometry Content Skills Assessments Standards A. Isometry A.1 Define and identify the terms: transformation, preimage, image, and corresponding parts A.2 Identify translations, reflections, rotations and dilations visually A.3 Classify transformations as isometry or not A.4 Apply transformations to tessellations (regular and Escher) Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.2 1.10 6.3 6.4 6.5 6.6 6.7 6.8 B. Reflection C. Rotation D. Translation E. Composition B.1 Identify and define reflection, line of reflection, and lines of symmetry B.2 Give coordinates of an image under reflection C.1 Identify and define rotation, center of rotation, angle of rotation, and rotational symmetry C.2 Identify a rotation as equivalent to reflections over two intersecting lines D.1 Identify and define translations, vector, and component forms D.2 Identify a translation as equivalent to reflections over two parallel lines D.3 Apply transformations to figures in the coordinate plane using matrices and using parallelograms D.4 Compute the magnitude and direction of a resultant vector using direct measurement on scale drawing, using the Pythagorean Theorem if perpendicular E.1 Define composition and glide reflection E.2 Perform a glide reflection in a coordinate plane HONORS Geometry Unit # 8 Similarity (3 weeks) Topic Geometry Content Skills Assessments Standards A. Review ratio, proportion, & reducing a square root A.1 Solve ratio and proportions A.2 Solve real-life problems using ratio and proportion B. Similar polygons B.1 Identify and construct similar polygons B.2 Identify similar triangles using AA~, SSS~, & SAS~ B.3 Use similar polygons to solve real life problems Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.9 1.10 2.6 3.8 3.9 4.6 6.3 6.4 7.4 C. Segments of similar polygons D. Dilations C.1 Calculate segment lengths using proportionality theorems C.2 Calculate segment lengths using geometric mean E. Self-similarity D.1 Identify and perform dilations using straightedge/compass and using coordinates D.2 Use scale factor to determine segment lengths of similar figures E.1 Identify and define self-similarity E.2 Perform an iteration of a fractal E.3 Locate self-similarity in Pascal's triangle and the Golden Rectangle HONORS Geometry Unit # 9 Right Triangle & Trigonometry (3 weeks) Topic Geometry Content Skills Assessments Standards A. Similar Right Triangles A.1 Solve proportions using similar right triangle created by the altitude to the hypotenuse A.2 Find side lengths of right triangles using geometric mean theorems Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.1 1.2 1.8 1.9 1.10 2.6 3.1 3.6 3.10 3.11 3.12 B. Pythagorean Theorem C. Special Right Triangles D. Trigonometry E. Vectors B.1 Reduce and rationalize radicals B.2 Find the missing side of a right triangle using the Pythagorean Theorem B.2 Prove the Pythagorean Theorem B.3 Classify right triangles as acute, right, or obtuse using the Converse of the Pythagorean Theorem B.4 Solve real-world problems using the Pythagorean Theorem C.1 Find the missing side lengths of a 45-45-90 triangle C.2 Find the missing side lengths of a 30-60-90 triangle D.1 Find sine, cosine, and tangent ratios of a right triangle D.2 Calculate the acute angle measures from trigonometric ratios D.3 Solve real-world problems using trigonometry with indirect measurement D.4 Solve right triangles using two sides of a right triangles D.5 Solve right triangles using one side and an acute angle of a right triangle E.1 Find the magnitude of a vector E.2 Find the direction of a vector E.3 Identify equal and parallel vectors E.4 Add vectors using the parallelogram method E.5 Calculate the sum of two vectors HONORS Geometry Unit # 10 Areas of Polygons and Circles (3 weeks) Topic Geometry Content Skills Assessments Standards A. Angles of Polygons A.1 Calculate the sum of the measures of a polygon A.2 Calculate each interior angle of a regular polygon A.3 Calculate an exterior angle of a regular polygon A.4 Calculate the number of sides of a polygon A.5 Calculate the measure of the central angle of a regular polygon Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.1 1.8 1.9 2.6 2.7 3.1 3.2 3.3 3.4 3.5 3.6 3.8 3.11 3.12 4.1 4.2 4.3 4.4 4.5 4.6 5.1 5.2 5.3 5.4 B. Areas of Regular Polygons C. Similar Figures D. Areas of Circles E. Geometric Probability F. Networks B.1 Calculate the area of an equilateral triangle B.2 Identify and calculate the length of the apothem B.3 Calculate the area of a regular polygon C.1 Calculate side lengths, perimeters, and areas of similar figures C.2 Compare perimeters and areas of similar figures using scale factor D.1 Calculate the perimeter of a circle D.2 Calculate arc length and central angle measure for a sector D.3 Calculate the area of a circle and a sector E.1 Calculate the areas of composite figures E.2 Calculate the geometric probability of a composite figure F.1 Define basic terms related to networks F.2 Determine if a network is traversable F.3 Apply Euler's Formula for networks HONORS Geometry Unit # 11 Surface Area and Volume (3 weeks) Topic Geometry Content Skills Assessments Standards A. Euler's Theorem A.1 Define polyhedron and related terms A.2 Identify types of polyhedra A.3 Apply Euler's Theorem to polyhedral Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.9 1.10 2.7 3.1 3.2 3.3 3.4 3.5 3.6 3.10 3.11 3.12 4.1 4.2 4.3 4.4 4.5 4.6 5.1 5.2 7.1 7.2 7.3 7.4 7.5 7.6 B. Surface Areas C. Volumes B. Calculate the surface areas of prisms, cylinders, pyramids, cones, and spheres D. Similar Solids E. Drawing 1. Cross sections 2. Isomorphic 3. Orthographic C. Calculate the volumes of prisms, cylinders, pyramids, cones, and spheres D.1 Define similar solids D.2 Compare and determine ratios of surface areas of similar solids D.3 Compare and determine ratios of volumes of similar solids E.1 Sketch cross sections of solids E.2 Sketch isometric views of solids E.3 Sketch orthographic views of solids HONORS Geometry Unit # 12 Circles (3 weeks) Topic Geometry Content Skills Assessments Standards A. Terminology A.1 Define terms relating to circles B. Tangents, Secants, Arcs, and Chords B.1 Calculate lengths of tangents, secants, and chords B.2 Determine the number of degrees in a central angle B.3 Calculate measures and lengths of arcs Oral questions Textbook exercises Worksheets Projects Unit Test (matching, multiple choice, open response) 1.2 1.9 1.10 5.1 5.2 5.3 5.4 5.5 5.6 5.7 7.1 7.2 7.3 C. Inscribed Angles D. Segment Lengths in Circles C.1 Calculate the measure of an inscribed angle or an intercepted arc C.2 Calculate the measures of the angles of an inscribed polygon E. Equations D.1 Determine lengths of secant segments and tangent segments E.1 Write and Identify the equation of a circle