Student Learning Goals for Geometry
Geometry students will:
 confront complexity with confidence
 make connections between all aspects of the curriculum
 apply skills and understanding to new situations
 analyze characteristics and properties of two- and three-dimensional shapes
 solve novel problems using visualization, spatial reasoning, and modeling
 develop deductive reasoning skills
Differentiation- Instruction is characterized by variations in:*Content, *Open-ended tasks, * Pacing,
*Complexity of thought, *Student choice, *Product outcomes
Deductive Reasoning and
Skills and Process
Proofs
Using internal and external resources
Students will:
Students will:
 Use the language, notation,  Cull data that are secondary to, analogous to, and consequent to given
and format of logic and
information
proofs
 Develop mental constructions, patterns, and images of geometric and
 Deduce truth values and
algebraic connections
tables for statements:
 Reshape complex subject matter into straightforward usable information
conditional, biconditional, In addition to recognizing and applying the properties, postulates, theorems,
conjunctions, and
and corollaries associated with the following topics and subtopics, students
disjunctions
examine each topic from the perspective of definition, classification,
 Create, label, alter, and/or
congruence, similarity, and measurement.
add to diagrams reflecting Specific topics include:
the original figure, givens, Points, lines, and planes
and proven information
 undefined terms
 Use previously learned
 collinear, coplanar
algebraic properties
 segments, rays
 Prove using several paths
 intersecting, skew, parallel, and perpendicular lines
 Prove using direct,
Angles
indirect, and transitive
 adjacent, vertical
logic
 complementary, supplementary, angles, and linear pairs
 Recognize and use patterns  angles formed by perpendicular lines and parallel lines, including angles
of proving
formed by a transversal and parallel lines
 Know and correctly use
Triangles
the key postulates,
 relationship between sides and angles of equilateral, isosceles, and scalene
theorems, properties, and
triangles
definitions relating to
 angle relationships including sum of angle measures and measure of
points, lines, angles,
exterior angles
triangles, quadrilaterals,
 side sums and mid-segments
circles, and solids
 triangle inequality
 Write formal proofs
 right triangles, special right triangles, Pythagorean Theorem and its
Constructions and Diagrams
converse, and Pythagorean triples
Students will:
 right triangle trigonometry
 Draw and label diagrams
 ratios representing tangents of angles, tangents of angles, ratios
to specification
representing sines of angles,
 Construct congruent
 sines of angles, ratios representing cosines of angles, cosines of angles
figures
 angle of elevation/angle of depression.
 Construct bisectors
 medians, altitudes, angle bisectors, and perpendicular bisectors
 Construct figures with
 points of concurrency
Peabody
School
specified relationships
Construct figures with
specified measures
 Construct figures to
demonstrate theorems
 Use construction tools and
techniques to find specific
points
 Develop new constructions
Specific constructions include:
 congruent line segment
 parallel line through a
point
 perpendicular bisector of a
segment
 perpendicular from a line
at a point
 perpendicular from a line
through a point
 perpendicular from the end
point of a ray
 bisect an angle
 congruent angle
 30° and 90° angle
 congruent triangle
 equilateral triangle
 isosceles triangle
 30-60-90 triangle
 triangle given SSS, ASA,
and SAS
 triangle medians and
altitudes
 incircle
 circumcircle
 circle, given three points
 tangent at a point on circle
 tangent through an
external point
 foci of a given ellipse
 use construction
techniques to find:
incenter, orthocenter,
circumcenter, centroid,
center of circle
 ellipse with string and pins
(non-Euclidean)
 find center of circle using
right angles (nonEuclidean)

 perimeter and area of triangles using sides and/or radii and apothems
Quadrilaterals
 relationships among sides, angles, and diagonals of parallelograms
including the special parallelograms: rectangles, rhombi, and squares
 additional parallel line theorems
 interior and exterior angle measures of regular polygons
 relationships among sides, angles, medians, and diagonals of trapezoids
and isosceles trapezoids
 relationships among sides, angles, and diagonals of parallelograms,
rectangles, rhombi, kites, triangles, trapezoids, composite figures, and
regular polygons
 perimeter and area of studied polygons including regular quadrilaterals
using sides and/or radii and apothems
 incircles/inscribed polygons and circumcircles
Circles
 chords, secants, diameter, radii - concentrics
 tangents, points of tangency
 angles: arcs, chords and central angles, interior, exterior, and inscribed
 major, minor, and adjacent arcs: angle and arc measure
 inscribed angles and intercepted arcs
 chords, intersecting chords, tangents, and intercepted arcs
 secants, tangents, and measures of intercepted arcs
 relationships of measures of segments: secants, chords, external, tangent
 circumference and area
 relationships between congruent chords and their minor arcs, a tangent line
and a radius, and congruent tangent segments
Solids
 altitudes, bases, lateral faces, lateral edges
 relationships among perimeter, base(s), height, lateral/surface area, and
volume
 prisms: right triangular, oblique
 pyramids
 cones
 cylinder
 spheres
 nets: draw and create, identify polyhedra by nets, determine surface area
using nets
Transformations/ Symmetry:
 reflections, translations, rotations
 isometry/congruence mapping
 dilations (including scale factors)/similarity mapping
 composite mapping
 identity and inverse
 multiple transformations
 relationships between reflections and rotations and between reflections and
translations
 line, point, rotational, translational, glide reflection, plane
 axis of symmetry