Download SCS Objectives

RCS Geometry Honors Pacing Guide
SCS Objectives
Essential Questions
Key Concepts
# Days
1.02 Use length, area, and volume of
geometric figures to solve problems.
2.01 Use logic and deductive
reasoning to draw conclusion and
solve problems.
2.02 Apply properties, definitions,
and theorems of angles and lines to
solve problems and write proofs
2.03 Apply properties, definitions,
and theorems of two-dimensional
figures to solve problems and write
proofs.
What is inductive reasoning and how can you use it to find
solutions?
How can you find basic geometry terms within different
figures?
How do you use the distance formula to measure points,
lines, etc.?
What are different angles and their parts?
How can you bisect and angle/segment?
What is the perimeter and area of common figures?
Patterns
Inductive reasoning
Point, lines, & planes
Segments
Angles
Segment & angle bisectors
Angle pair relationships
Perimeter
Circumference
Area
4
2.01 Use logic and deductive
reasoning to draw conclusion and
solve problems.
2.02 Apply properties, definitions,
and theorems of angles and lines to
solve problems and write proofs.
How can you use postulates about points, lines, and planes to
analyze real-life objects?
How do you rewrite postulates in a form suitable for
problems solving?
How do you determine whether a logic statement is valid?
How can you use algebra to solve geometric equations?
How can you prove statements about segments in real-life
situations?
How can you use properties of angle congruence to prove
properties about pairs of angles?
Conditional statements
Biconditional statements
Deductive reasoning
Reasoning w/ algebra
properties
Proving segment statements
Proving angle statements
4
2.01 Use logic and deductive
reasoning to draw conclusion and
solve problems.
2.02 Apply properties, definitions,
and theorems of angles and lines to
solve problems and write proofs.
How do you describe lines and planes in real-life objects?
Can you write and use different type of proofs and show how
this is done?
How can you prove and use results about parallel lines and
transversals to understand the world around you?
How do you know when lines are parallel?
Can you use (and demonstrate the use of) properties of
parallel lines?
How can you write an equation of a line parallel to a given
line in a coordinate plane?
Lines
Angles
Perpendicular lines proof
Parallel lines
Transversals
Proving lines are parallel
Properties of parallel lines
Parallel lines in a coordinate
plane
Perpendicular lines in a
coordinate plane
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RCS Geometry Honors Pacing Guide
How do you use slope to decide whether lines are
perpendicular?
Can you find the distance from a point to a line?
2.01 Use logic and deductive
reasoning to draw conclusion and
solve problems.
2.02 Apply properties, definitions,
and theorems of angles and lines to
solve problems and write proofs.
2.03 Apply properties, definitions,
and theorems of two-dimensional
figures to solve problems and write
proofs.
How can you classify triangles by their sides and angles?
How do you identify congruent figures and corresponding
parts?
How do you prove triangles are congruent using AAS
theorem, SSS, SAS, and ASA postulates?
How do you use congruent triangles to plan and write
proofs?
When are the properties of isosceles, equilateral, and right
triangles applied?
How can you prove triangles are congruent using coordinate
geometry?
Triangles
Angles of triangles
Congruence in triangles
SSS
SAS
ASA
AAS
Using congruent triangles
Isosceles
Equilateral
Right triangles
Triangles & coordinate proof
5
1.02 Use length, area, and volume of
geometric figures to solve problems.
2.02 Apply properties, definitions,
and theorems of angles and lines to
solve problems and write proofs.
2.03 Apply properties, definitions,
and theorems of two-dimensional
figures to solve problems and write
proofs.
How can you use perpendicular and angle bisectors to decide
where a hockey goalie should be placed?
How can you find the perpendicular and angle bisector of a
triangle?
Where can you use properties of medians and altitudes?
How do you use properties of midsegments of a triangle?
Why would you compare the length of the side or the
measures of angles of a triangle?
How can you show that you understand indirect proofs?
Perpendiculars & bisectors
Bisectors of a triangle
Medians of a triangle
Altitudes of a triangle
Midsegment theorem
Inequalities of one triangle
Indirect proof-inequalities 2
triangles
7
1.02 Use length, area, and volume of
geometric figures to solve problems.
2.02 Apply properties, definitions,
and theorems of angles and lines to
solve problems and write proofs.
2.03 Apply properties, definitions,
and theorems of two-dimensional
How do you identify different polygons?
Can you find an unknown measure of an angle of a
quadrilateral?
How do you use the properties of a parallelogram?
How can you use coordinate geometry with parallelograms?
What are some properties of rectangles, squares, and
rhombuses and how can you use them to simplify real-life
Polygons (angle measures)
Properties of parallelograms
Proofs
• Quadrilaterals
• Parallelograms
Rhombus
Rectangles
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RCS Geometry Honors Pacing Guide
figures to solve problems and write
proofs.
tasks?
What are the properties of trapezoids and kites?
How can you prove that a quadrilateral is a special type of
quadrilateral?
What are the areas of rectangles, kites, parallelograms,
squares, triangles, trapezoids, and rhombuses?
Squares
Trapezoids & kites
Special quadrilaterals
Areas of triangles
Areas of quadrilaterals
1.02 Use length, area, and volume of
geometric figures to solve problems.
2.03 Apply properties, definitions,
and theorems of two-dimensional
figures to solve problems and write
proofs.
3.02 Use matrix operations (addition,
subtraction, multiplication, and
scalar multiplication) to describe the
transformation of polygons in a
coordinate plane.
What is the ration of two numbers?
Can you understand properties and proportions?
How do you identify similar polygons and use properties of
similar polygons?
How would you prove tow triangles are similar using
definitions and AA similarity postulate?
Ratio
Proportions
Problem solving w/
proportions
Similar polygons
Similar triangles
4
1.01 Use the trigonometric rations to
model and solve problems involving
right triangles.
1.02 Use length, area, and volume of
geometric figures to solve problems.
2.02 Apply properties, definitions,
and theorems of angles and lines to
solve problems and write proofs
2.03 Apply properties, definitions,
and theorems of two-dimensional
figures to solve problems and write
proofs.
How can you solve problems involving similar right
triangles formed by the altitude drawn to the hypotenuse of a
right triangle?
What is the Pythagorean theorem?
How do you use side lengths to classify triangles by their
angle measure?
When can you find side lengths of special triangles?
How do you find trigonometric rations of an acute angle?
How do you find the magnitude, direction, and sum of a
vector?
Similar right triangles
Pythagorean theorem
Converse of Pythagorean
theorem
Special Right triangles
Trigonometric Ratios
Solving Right Triangles
Vectors
8
1.02 Use length, area, and volume of
geometric figures to solve problems.
2.02 Apply properties, definitions,
How can you identify and use properties of tangents of
circles?
How can you use properties of arcs and chords of circles to
Circles
Tangents to circles
Arcs
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RCS Geometry Honors Pacing Guide
and theorems of angles and lines to
solve problems and write proofs
2.03 Apply properties, definitions,
and theorems of two-dimensional
figures to solve problems and write
proofs.
solve problems?
How can you use properties of inscribed angles and inscribed
polygons of circles to reach conclusions about angles?
How can you use angles formed by tangents, chords, and
secants?
How do you find the length of segments of tangents, chords,
and lines that intersect a circle?
How do you find and graph the equations of a circle?
How do you draw loci in a plane that satisfy one or more
conditions?
Chords
Inscribed angles
Angle relationships
Segment lengths in circles
Equations of circles
loci
1.02 Use length, area, and volume of
geometric figures to solve problems.
2.02 Apply properties, definitions,
and theorems of angles and lines to
solve problems and write proofs
2.03 Apply properties, definitions,
and theorems of two-dimensional
figures to solve problems and write
proofs.
How can you find the measure of interior and exterior angles
of a polygon?
How do you find the areas of equilateral triangles and other
polygons?
How would you compare perimeters and areas of similar
figures?
How can you find the circumference of a circle and the
length of an arc of a circle?
What is geometric probability?
Area of regular polygons
Perimeters of similar figures
Area of similar figures
Circumference & Arc length
Areas of Circles & sectors
Geometric probability
7
1.02 Use length, area, and volume of
geometric figures to solve problems.
2.03 Apply properties, definitions,
and theorems of two-dimensional
figures to solve problems and write
proofs.
2.04 Develop and apply properties of
solids to solve problems.
How can you use properties of polyhedra to solve problems?
How do you find the surface area of prisms and cylinders?
How do you find the volume of prisms and cylinders?
How do you find the surface area of pyramids and cones?
How do you find the volume of pyramids and cones?
How do you find the surface area and volume of a sphere?
How do you find the surface area and volume of similar
solids?
Exploring solids
Surface area & Volume
• Prisms
• Cylinders
Surface Area & Volume
• Pyramids
• Cones
Surface Area & Volume
• Spheres
Similar Solids
7
2.02 Apply properties, definitions,
and theorems of angles and lines to
How can you identify type of rigid transformations?
How can you use properties of reflection?
Rigid Motion in a plane
Reflections
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RCS Geometry Honors Pacing Guide
solve problems and write proofs.
3.01 Describe the transformation
(translation, reflection, rotation,
dilation) of polygons in the
coordinate plane in simple algebraic
terms.
3.02 Use matrix operations (addition,
subtraction, multiplication, and
scalar multiplication) to describe the
transformation of polygons in a
coordinate plane.
How do you relate rotations and rotational symmetry?
How do you use properties of translation?
How do you use properties of glide reflection?
How do you classify frieze patterns?
Rotations
Translation & vectors
Glide reflections
Compositions
Frieze Patterns