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Geometry 2023-2024
Unit 0 Pre Requisite Skills
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Solving Equations – include equations with fractions
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Parallel and Perpendicular Lines – slope formula, getting into y=, writing equations of parallel and perpendicular lines
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Writing Equations – given slope and y-intercept, given 2 points, etc
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Radicals and the Pythagorean Theorem – simplify radicals, add/sub/mult radicals
Unit 1 Basic Constructions
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Essential Skills – naming segments, points, rays, planes, angles, etc; classifying angles – acute, obtuse, right, straight; definitions of bisect, midpoint, etc.; classify triangles by angles and sides
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Equilateral Triangles construct equilateral and isosceles triangles, inscribed square and hexagon; copy segments
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Bisectors – copy and bisect an angle; construct perpendicular bisector
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Concurrences – construct circumcenter, incenter;and inscribe and circumscribe a circle about a triangle; concurrences theorems
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Concurrences - construct centroid, orthocenter concurrences theorems
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Parallel Lines and Apps – construct parallel lines
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Unit Test
Unit 2 Rigid Motion
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Essential Skills – identify reflections, translations, rotations, dilations, line of symmetry, point symmetry, rotational symmetry, angles of rotation, degree and order of rotation
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Rigid Motion Exploration – ABCD preservation method for rigid motion; orientation
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Coordinate Plane – transformation rules in the coordinate plane
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Sequences – compositions and identifying sequences of rigid motion
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Compositions – more compositions and sequences
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Applications
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Test
Unit 3 Unknown Angles
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Essential Skills writing good definitions; identifying complementary, supplementary, vertical, adjacent angles, alternate interior, alternate exterior, corresponding, interior on the same side angles; segment and angle addition; geometry’s undefined terms; reflexive, symmetric, and transitive postulates; auxiliary lines
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Finding Angles – small algebraic proofs with angles; sum of angles on a straight line is 180; the sum of adjacent angles around a point is 360; vertical angles are congruent
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Transversal Angles parallel lines angles and auxiliary lines
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Intro to Proofs – paragraph proofs, two column proofs, flowchart proofs
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Coordinate Proofs – proofs using midpoint and slope; parallel lines and perpendicular lines and relationships to slope
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Apps
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Test
Unit 4 Triangles
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Triangle Angles – sum of interior angles of a triangle theorem, exterior angle of a triangle theorem
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Isosceles Triangle Theorems – parts of an isosceles triangle; isosceles triangle theorems
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Inequalities – triangle inequality theorem; largest angle across from the longest side; exterior angle inequality theorem
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Concurrence on Coordinate Plane – determine the equation of a perpendicular line; centroid formula; find the circumcenter algebraically
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Concurrence off Coordinate Plane – revisit constructing concurrences; divide a segment into congruent pieces
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Quest
Unit 5 Triangle Congruence
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Triangles Congruence Statements – identifying corresponding parts
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Congruence Theorems – AAS, ASA, SSS, SAS, no AAA, ASS
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Congruence Theorems Part 2 – more proofs with triangle congruence
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CPCTC – proofs with CPCTC
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HL – hypotenuse leg theorems
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Isosceles Triangle Proofs – proofs using isosceles triangle theorems
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Overlapping Triangles
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Apps
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Unit Test
Midterm
Unit 6 Similarity and Dilations
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Essential skills: derive distance formula and investigate (graphically). Use distance formula to find area and perimeter of figures.
(HW: Prove Isosceles Right Triangle)
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Real life Apps: Ratios, proportions and scale factors (Find the point on a directed line segment between two given points that partitions the segment in a given ratio - board is cut...) 2-1 (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios)
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Introduce Similarity and Dilations
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Similarity theorems (AA ASA SAS)-proofs
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Show how to find the center of dilation
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Proofs with dilation
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Triangle proportionality and mid-segment theorem
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Dilation Proofs
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Geometric Mean
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Apps
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Test
Unit 7: Right triangle Trig
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Essential skills:
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vocabulary of a right triangle (OHA) and Pythagorean theorem
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Basic trig ratios: set up trig ratios
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Real life apps
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Solving trig ratios, real life apps
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(Explain and use the relationship between the sine and cosine of complementary angles.)
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Apps - trig and Pythagorean thm modeling problems
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Quest
Unit 8: Quads
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Essential skills: Quadrilateral Lab
Find lines of symmetry for each quadrilateral
Matrix for HW
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Algebraic applications using properties
Thm sheets (If and only if) necessary and sufficient
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Coordinate Geometry proofs: review triangles, trapezoids and kites
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Coordinate Geometry proofs: review trapezoids, parallelograms
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Euclidean Proofs (mini proofs based on diagrams with markings)
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Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
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NYSED: Theorems include but are not limited to the listed theorems. Example: rhombus is a parallelogram with perpendicular diagonals.
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Euclidean and Transformation proofs
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Applications
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Test
Unit 9: Geometric measurement
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Essential Skills 2-Dimensional- multi-step problems; Hand out Formula Sheet; Unit Conversions (Hand out NYS reference sheet)
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Volume: prisms (rectangular, triangular, etc.) use reference sheets, applications,work backwards, and derive formulas
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Volume: pyramids
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Volume: non polyhedrons - spheres, cylinders, cones (reference sheet, applications), derive formulas
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Cross-section of prisms, pyramids, cylinders, cones, spheres (include Cavalieri’s principle)
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Application problems
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Test HW: circle vocab ppt
Unit 10: Circles
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Essential Skills - equation of circle, graph circle on coordinate plane; derive the equation of a circle in center-radius form by completing the square
Quiz: circle vocab (ppt)
Do Now: construct figures in a circle: equilateral triangle, hexagon and square
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Angles of a circle
do now: tangents and secants
HW: flashcards
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Segments in a circle-chords equidistant and parallel chords, tangents, secants, chord lengths
Do now: quadrilaterals inscribed in a circle and similarity of concentric and other circles
HW: flashcards
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Arc length and area of sector, derive the formula for the area of sectors, radian measure, S=OR
Do Now: degrees and radians
Quiz on circle angles
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Circle Proofs
Do Now: intersecting chord similar triangles proof and 2 secants proof
Practice: big circle problem
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Apps
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Test
Geometry Regents Exam in June
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