At a Glance:
An Overview of Topics by Unit: (Not implied to be in a linear order and elaboration on each topic can be found
throughout the document)
Unit 1:
Section I:
Undefined terms
Basic Geometric Vocabulary
Classify polygons by sides. Define convex, concave, equilateral, equiangular, regular
Postulates
Basic diagram interpretation
Basic constructions
Angle Notation and Relationships
Section II:
Counter example/inductive/deductive reasoning
Conditional and Bi-conditional Statements
Detachment/Syllogism
Algebraic Proofs
Basic Proofs (Two-Column, Flow, Paragraph) using segment addition postulate, angle addition postulate,
reflexive, symmetric, and transitive properties, linear pair postulate, definitions, vertical angle congruence
theorem, etc.
Parallel lines and angles formed by transversals (with proofs)
Section III:
Classify and triangles, find perimeter and area and prove their properties (on coordinate plane)
Classify quadrilaterals, find perimeter and area and prove their properties (on coordinate plane)
Midpoint and distance formula
Directed line segment in a ratio
Coordinate geometry
*Modeling where appropriate
Unit 2:
Define rigid transformations and isometry
Use miras, patty paper, software, protractors and rulers to perform reflections, rotations and translations on coordinate
plane and not on coordinate plane
Rotational/Reflectional symmetry
Define reflections, rotation sand translations in formal geometric terms (see HSG- CO. A.4)
Find a sequence of transformations that carry a pre-image to an image
Use rigid transformations to prove congruence-Triangles are congruent iff a series of rigid transformations map one
onto the other and if the corresponding angles and corresponding sides of the two triangles are congruent.
Dilations (in coordinate plane and out)… Similarity may be introduced here
*Modeling where appropriate
Unit 3:
Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms
of rigid motions.
Triangle Proofs using SSS, SAS, HL, ASA, AAS, CPCTC (Two-Column, Flow Proof, Paragraph)
Prove properties of triangles
Prove properties of quadrilaterals using triangles
*Modeling where appropriate
Unit 4:
Ratios, proportions and properties of proportions
Properties of dilations, scale factors using center of dilations and rays (with a ruler and software)
Explain if figures are similar using similarity transformations and definitions. Find values for missing pieces of similar
figures using definition
Establish AA, SSS, SAS criteria for proving triangles similar
Prove Pythagorean Theorem using similarity
Midsegment Theorem
*Modeling where appropriate
Unit 5:
Understand and develop trigonometric ratios using triangle similarity
Use trigonometric ratios and Pythagorean Theorem to solve right triangles (including problems with angles of elevation
and depression)
Explain relationship between sine/cosine of complementary angles
Honors:
Prove law of sines and cosines, use to solve applied problems
Derive formula 1/2absinC for area of triangle
*Modeling where appropriate
Unit 6:
*Points of concurrency?*(Construct inscribed and circumscribed circles of triangle)
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Prove that all circles are similar
Basic circle vocabulary and arc notation (10.1-10.2 in textbook)
Identify relationships between radii, chords, secants, tangents and angles in circles (10.3-10.6 in textbook)
Equations of circles in standard form (including completing the square)/Use coordinate geometry and circles in the
coordinate plane
Prove properties of inscribed quadrilateral and right triangle in a circle
Arc lengths and area of sectors using proportions and radians
Honors:
Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances
from the foci is constant.
Construct a tangent line from a point outside a given circle to the circle.
*Modeling where appropriate
Unit 7:
Find volume of cylinders, pyramids, cones, spheres, prisms
Informal proofs of volume formulas
Cross sections and three dimensional shapes created by two dimensional rotations
Density problems based on area and volume
Honors:
Cavalieri’s principle
*Modeling where appropriate