
Geometry 20232024
Unit 0 Pre Requisite Skills

Solving Equations – include equations with fractions

Parallel and Perpendicular Lines – slope formula, getting into y=, writing equations of parallel and perpendicular lines

Writing Equations – given slope and yintercept, given 2 points, etc

Radicals and the Pythagorean Theorem – simplify radicals, add/sub/mult radicals
Unit 1 Basic Constructions

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

Equilateral Triangles construct equilateral and isosceles triangles, inscribed square and hexagon; copy segments

Bisectors – copy and bisect an angle; construct perpendicular bisector

Concurrences – construct circumcenter, incenter;and inscribe and circumscribe a circle about a triangle; concurrences theorems

Concurrences  construct centroid, orthocenter concurrences theorems

Parallel Lines and Apps – construct parallel lines

Unit Test
Unit 2 Rigid Motion

Essential Skills – identify reflections, translations, rotations, dilations, line of symmetry, point symmetry, rotational symmetry, angles of rotation, degree and order of rotation

Rigid Motion Exploration – ABCD preservation method for rigid motion; orientation

Coordinate Plane – transformation rules in the coordinate plane

Sequences – compositions and identifying sequences of rigid motion

Compositions – more compositions and sequences

Applications

Test
Unit 3 Unknown Angles

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

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

Transversal Angles parallel lines angles and auxiliary lines

Intro to Proofs – paragraph proofs, two column proofs, flowchart proofs

Coordinate Proofs – proofs using midpoint and slope; parallel lines and perpendicular lines and relationships to slope

Apps

Test
Unit 4 Triangles

Triangle Angles – sum of interior angles of a triangle theorem, exterior angle of a triangle theorem

Isosceles Triangle Theorems – parts of an isosceles triangle; isosceles triangle theorems

Inequalities – triangle inequality theorem; largest angle across from the longest side; exterior angle inequality theorem

Concurrence on Coordinate Plane – determine the equation of a perpendicular line; centroid formula; find the circumcenter algebraically

Concurrence off Coordinate Plane – revisit constructing concurrences; divide a segment into congruent pieces

Quest
Unit 5 Triangle Congruence

Triangles Congruence Statements – identifying corresponding parts

Congruence Theorems – AAS, ASA, SSS, SAS, no AAA, ASS

Congruence Theorems Part 2 – more proofs with triangle congruence

CPCTC – proofs with CPCTC

HL – hypotenuse leg theorems

Isosceles Triangle Proofs – proofs using isosceles triangle theorems

Overlapping Triangles

Apps

Unit Test
Midterm
Unit 6 Similarity and Dilations

Essential skills: derive distance formula and investigate (graphically). Use distance formula to find area and perimeter of figures.
(HW: Prove Isosceles Right Triangle)

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...) 21 (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios)

Introduce Similarity and Dilations

Similarity theorems (AA ASA SAS)proofs

Show how to find the center of dilation

Proofs with dilation


Triangle proportionality and midsegment theorem

Dilation Proofs

Geometric Mean

Apps

Test
Unit 7: Right triangle Trig

Essential skills:

vocabulary of a right triangle (OHA) and Pythagorean theorem


Basic trig ratios: set up trig ratios

Real life apps


Solving trig ratios, real life apps

(Explain and use the relationship between the sine and cosine of complementary angles.)


Apps  trig and Pythagorean thm modeling problems

Quest
Unit 8: Quads

Essential skills: Quadrilateral Lab
Find lines of symmetry for each quadrilateral
Matrix for HW

Algebraic applications using properties
Thm sheets (If and only if) necessary and sufficient

Coordinate Geometry proofs: review triangles, trapezoids and kites

Coordinate Geometry proofs: review trapezoids, parallelograms

Euclidean Proofs (mini proofs based on diagrams with markings)

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.

NYSED: Theorems include but are not limited to the listed theorems. Example: rhombus is a parallelogram with perpendicular diagonals.

Euclidean and Transformation proofs

Applications

Test
Unit 9: Geometric measurement

Essential Skills 2Dimensional multistep problems; Hand out Formula Sheet; Unit Conversions (Hand out NYS reference sheet)

Volume: prisms (rectangular, triangular, etc.) use reference sheets, applications,work backwards, and derive formulas

Volume: pyramids

Volume: non polyhedrons  spheres, cylinders, cones (reference sheet, applications), derive formulas

Crosssection of prisms, pyramids, cylinders, cones, spheres (include Cavalieri’s principle)

Application problems

Test HW: circle vocab ppt
Unit 10: Circles

Essential Skills  equation of circle, graph circle on coordinate plane; derive the equation of a circle in centerradius form by completing the square
Quiz: circle vocab (ppt)
Do Now: construct figures in a circle: equilateral triangle, hexagon and square

Angles of a circle
do now: tangents and secants
HW: flashcards

Segments in a circlechords equidistant and parallel chords, tangents, secants, chord lengths
Do now: quadrilaterals inscribed in a circle and similarity of concentric and other circles
HW: flashcards

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

Circle Proofs
Do Now: intersecting chord similar triangles proof and 2 secants proof
Practice: big circle problem

Apps

Test
Geometry Regents Exam in June
