Honors Geometry Syllabus
Lesson/ Topic
Skill/ Objective
Unit 1: Points, lines, and planes
Points, lines, and planes
Be able to state basic terms of Geometry and understand why some of
the definitions are intuitive
Segments, rays, and
Be able to use the proper terminology and symbolically represent
distance
segments and rays
Be able to draw representations of Geometric concepts
Angles
Know the different types of angles and parts of angles
Postulates and theorems Be able to compare and contrast the requirements for points, lines,
relating points, lines, and planes
planes
Understand the postulates and theorems that go along with points, lines,
and planes
Unit 2: Deductive reasoning
If-Then statements and
Be able to recognize the parts of conditional statements
converse
Be able to provide counterexamples
Properties
Be able to recall the properties from Algebra and Geometry
Be able to use the properties to justify Geometric statements
Proving theorems
Be able to use bisectors for angles and segments
Be able to formulate their own steps for two-column proofs
Special pairs of angles
Be able to prove and use vertical angles
Perpendicular lines
Be able to use perpendicular bisectors
Be able to state properties of perpendicular bisectors
Planning a proof
Be able to do proofs from scratch on their own
Unit 3: Parallel Lines and Planes
Definitions
Students will be familiar with the definitions for special angles of lines cut
by transversals
Properties of parallel
Know the special angles of parallel lines and their relationships
lines
Proving lines parallel
Be able to prove that lines are parallel based on the angles
Angles of a triangle
Will know that a triangle has 180° in its angles
Be able to apply the exterior angle relationship
Angles of a polygon
Be able to use the polygon angle sum formula and the exterior angle
relationships
Inductive reasoning
Be able to recognize patterns in numbers and geometric diagrams
Unit 4: Congruent Triangles
Congruent figures
Be able to define and recognize congruent polygons
Be able to use the corresponding parts of congruent polygons
Proving triangles
Be able to prove triangles congruent with three postulates
congruent
Using congruent triangles Be able to give justification for triangles to be congruent
Isosceles triangle
Be able to apply the properties of isosceles triangles and know when to
theorems
use them
Alternate methods for
proving triangles
congruent
Using more than one pair
of congruent triangles
Medians, altitudes, and
perpendicular bisectors
Unit 5: Quadrilaterals
Properties of
parallelograms
Proving quadrilaterals
are parallelograms
Theorems involving
parallel lines
Special parallelograms
Be able to state and use other ways of proving triangles congruent
including HL and AAS
Be able to use one pair of congruent triangles to get another pair
Be able to apply definitions of medians, altitudes, perpendicular bisectors
Be able to state and apply the theorems about perpendicular bisectors
and angle bisectors
Be able to state the definitions and properties of parallelograms
Be able to prove certain quadrilaterals are parallelograms
Be able to apply the theorem involving the midsegment of a triangle
Be able to classify different types of parallelograms, and identify their
properties
Trapezoids
Be able to apply the definition of a trapezoid and compare and contrast
its properties to other special parallelograms
Unit 6: Inequalities in Geometry
Inequalities
Be able to state and apply properties of inequalities
Inverses and
Be able to state the contrapositive and inverse of a conditional statement
contrapositives
Indirect proofs
Be able to prove through contradition
Inequalities for one
Be able to understand and use inequality theorems and corollaries for
triangle
one triangle
Inequalities for two
Be able to understand and use inequality theorems and corollaries for
triangles
two triangles
Unit 7: Similar Polygons
Ratio and proportion
Be able to recall properties of ratios from algebra, and express ratios in
simplest form
Properties of proportions Be able to solve and manipulate proportions
Similar polygons
Be able to state and apply theorems for similar polygons
A postulate for similar
Use AA postulate to set up proportions involving similar triangles
triangles
Theorems for similar
Be able to use ASA and SAS similarity theorems to prove two triangles are
triangles
similar
Proportional lengths
Be able to recognize and utilize theorems involving proportions in
triangles
Unit 8: Right Triangles
Similarity in right
Be able to determine the geometric mean between two numbers, and
triangles
use geometric mean to find segments lengths when the altitude is drawn
to the hypotenuse of a right triangle
The Pythagorean
Be able to apply the Pythagorean Theorem to find side lengths of a
Theorem
triangle
The converse of the
Pythagorean Theorem
Special right triangles
Be able to classify triangles as acute, obtuse, or right
Be able to recognize special right triangles and determine the lengths of
unknown sides
The tangent ratio
Be able to use the tangent ratio to find unknown values within right
triangles
The sine and cosine
Be able to use the sine and cosine ratios to find unknown values within
ratios
right triangles
Applications of right
Be able to apply the trig functions to solve real-world application
triangle Trigonometry
problems
Unit 9: Coordinate Geometry (from chapter 13)
The distance formula
Be able to develop and apply the distance formula
Be able to use the distance formula to establish properties of a twodimensional shape
Slope of a line
Be able to calculate the slope of a line given two coordinate points
Be able to apply the slope of a line to solve problems
Parallel and
Be able to determine whether lines are parallel or perpendicular based on
perpendicular lines
their slope values
Be able to analyze the slope between two points to establish properties
of a two-dimensional shape
The midpoint formula
Be able to calculate the midpoint of a line segment on a coordinate plane
Be able to use the midpoint formula to establish properties of a twodimensional shape
Graphing linear
Be able to graph a line using the standard or slope intercept form of an
equations
equation
Be able to graph an inequality using proper line graphing and shading
techniques
Unit 10: Circles (from chapter 9)
Basic terms
Be able to identify parts of circles and spheres
Tangent
Be able to apply theorems relating to tangents and radii of circles
Arcs and central angles
Be able to recognize and use relationships between arcs and central
angles
Arcs and chords
Be able to apply theorems about arcs and chords, and make conclusions
about their relationships
Inscribed angles
Be able to solve problems involving inscribed angles and their
relationships to their arcs
Other angles
Be able to solve problems using angles formed by chords, secants, and
tangents
Circles and lengths of
Be able to solve problems involving lengths of chords, secant segments,
segments
and tangent segments
Unit 11: Areas of Plane Figures
Areas of rectangles
Be able to differentiate square units from linear units
Be able to find the area of a rectangle
Be able to find the area of irregular figures
Areas of parallelograms,
Be able to utilize the formulas for areas of parallelograms, triangles, and
triangles, and rhombus
rhombuses
Areas of trapezoids
Areas of regular polygons
Be able to use the formula for the area of a trapezoid
Be able to find the apothem of a regular polygon, and use the apothem to
find the area of a regular polygon
Circumferences and
Be able to recall the formulas for circumference and area of a circle, and
areas of circles
apply those formulas to circles
Arc lengths and areas of
Be able to find the length of an arc and the area of a sector
sectors
Understand how arc length and area of sectors correlate to the entire
circumference and area
Ratios of areas
Be able to understand the relationship between the dimensions of figures
and units of area
Geometric probability
Be able to use geometry to determine the probability of certain outcomes
Unit 12: Areas and Volumes of Solids
Prisms
Be able to identify the parts of prisms and calculate their surface area and
volume
Pyramids
Be able to identify and label parts of a pyramid and apply the formulas for
their surface area and volume
Cylinders and cones
Be able to identify parts of cylinders and cones, calculate their volume
and surface area
Spheres
Be able to identify and label the parts of spheres and calculate their
surface area and volume
Areas and volumes of
Be able to apply the scale factors to make conclusions about similar solids
similar solids