Download Geometry - Saint Mary`s College High School

St. Mary's College High School
Geometry
Content
Points, Lines, and Planes and
Angles
Skills
Assessment
Essential Questions:
A1. Identify and Model points,
lines, and planes.
A2. Identify collinear and coplanar
points, and intersecting lines and
planes in space.
Write a short essay on the meaning
of Geometry and how it used in
everyday life.
• What notations represent different
sets of points?
• Why are some important
geometric terms left undefined?
• How is the distance calculated
between two points on a coordinate
plane?
• What is a polygon?
• What is congruence? Is it the
same as equals?
Big Ideas:
• Learning the meaning and use of
various geometric terms.
• Reviewing the distance formula,
and is application to set the
foundation for future uses.
• Learn to identify the different
polygons, and how to find their
perimeter.
B1. Measure segments and
determine accuracy of
measurements.
B2. Determine two line segments
are congruent.
Diagnostic check on some basic
Algebra skills (Formative
Assessment)
Review vocabulary terms, and use
a vocabulary builder. (Formative
Assessment)
C1. Calculate the distance between
two points using the distance
formula.
C2. Find the midpoint of a line
segment using the midpoint
formula.
Review nightly homework
assignments.
D1. Measure and classify angles.
D2. Identify congruent angles and
angle bisectors.
In-class examples, practice, and
worksheets.
(Formative Assessment)
E1. Identify and use special pairs
of angles.
E2. Identify perpendicular lines.
Short quiz.
(Summative Assessment)
Monitor progress of students during
class.
(Formative Assessment)
F. Identify, name, and find the
perimeter of polygons.
• Learn the difference and
similarities of congruence and
equals, and then apply to proofs in
the future.
G. Distinguish the difference
between congruence and equals.
Content
Reasoning and Proofs
Skills
Assessment
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Geometry
Content
Essential Questions:
• How are conditional statements
related to theorems in geometry?
• What is the role of postulates and
theorems in building geometry as a
mathematical system?
• What is a Proof? Why is Proof
important? How is proof used in
everyday life?
Big Ideas:
• We use conditional statements to
establish a logical process to
explain the use of Proofs.
- By learning the difference
between postulates and theorems,
students will be able to determine
their use of building a Proof.
Skills
A. Make conjectures based on
inductive reasoning, and find
counterexamples.
B1. Determine truth values of
conjunctions and disjunctions.
B2. Construct truth tables.
C1. Analyze and write statements
in if-then form.
C2. Write the converse, inverse,
and contrapositive of if-then
statements.
D. Determine valid conclusions,
using the Law of Detachment and
the Law of Syllogism.
Essential Questions:
• What does parallel mean
and how is it different from
perpendicular?
• What is a transversal?
Big Ideas:
Assessment
Short basic skills quiz.
Review nightly homework.
(Formative Assessment)
Monitor progress of students
during class.
(Formative Assessment)
In-class examples, practice and
worksheets.
(Formative Assessment)
Chapter 1 test, with open-ended
problems, with critical thinking
problems.
(Summative Assessment)
E. Identify and use basic
postulates and theorems to write
paragraph proofs.
Geometry crossword puzzle.
F1. Use algebra to write twocolumn proofs.
F2. Use properties of equality and
definitions in geometric proofs.
Construction problem, going
around a lake, to create a line
extension using perpendicular lines
and bisectors.
(Formative Assessment)
G. Write proofs involving segment
addition and segment congruence.
Parallel and Perpendicular Lines
St. Mary's College High School
H1. Write proofs involving
supplementary and complementary
angles.
H2. Write proofs involving
congruent and right angles.
Logic Matrix.
Chapter 2 Test with open-ended
and logic problems, two-column
proofs, and critical thinking
problems. (Summative
Assessment)
A1. Identify the relationships
between two lines and two planes.
A2. Name angles formed by a pair
of lines and a transversal.
B1. Use the properties of parallel
lines and transversals to determine
congruent and supplementary
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Geometry
Content
• The knowledge of parallel
and perpendicular lines are
demonstrated by the
definition of slope on a
coordinate plane.
Skills
angles.
B2. Use Algebra to find angle
measures.
St. Mary's College High School
Assessment
C. Find slopes of lines, and use it
to identify parallel and
perpendicular lines.
D1. Write an equation in slopeintercept form, of a line, given
information about its points, slope
or its graph.
D2. Solve problems by writing
equations.
Content
Parallel and Perpendicular LInes
Skills
Assessment
Essential Questions:
•
•
How do you prove that two
lines are parallel?
How is the distance
between two parallel lines
determined?
Big Ideas:
•
Review nightly homework
assignments.
E1. Recognize angle conditions
that occur with parallel lines.
E2. Prove that two lines are
parallel based on given angle
relationships.
In-class examples, practice, and
F. Apply the distance formula, find worksheets.
the distance between a point and a
(Formative Assessment)
line, and between two parallel
lines.
Short basic skills quiz.
To calculate the distance
between two parallel lines,
the distance formula, and
knowledge of slope, and
perpendicular must be
combined.
CONGRUENT TRIANGLES
Essential Questions:
Monitor progress of students during
class.
(Formative Assessment)
In-class critical thinking problems.
(Formative Assessment)
Chapter 3 test, with open-ended,
multiple choice, and critical
thinking problems.
(Summative Assessment)
A. Identify and classify triangles
by sides and angles.
B. Apply the Angles Sum
Theorem and the Exterior Angle
Theorems.
Chapter 4 test with open-ended
problems, two-column proofs, and
critical thinking problems.
(Summative Assessment)
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Geometry
Content
• What is a triangle, and how
are they classified?
•
What is necessary to prove
congruence between two
different triangles?
Big Ideas:
•
•
•
Triangle play a significant
role in geometry, so being
able to identify and classify
them is essential.
Proving triangles are
congruent involves the use
of theorems, properties, and
definitions.
Skills
St. Mary's College High School
Assessment
C1. Name and label
corresponding parts of congruent
triangles.
C2. Identify congruence
transformation.
D. Use the SSS, the SAS, the
ASA, and the AAS postulates and
theorems to test for triangle
congruence.
E. Understand that Corresponding
Parts of Congruent Triangles are
Congruent. (CPCTC)
F. Apply properties of isosceles
and equilateral triangles.
The understanding of
congruent parts of a triangle
is essential when proving
congruence.
Content
Skills
Assessment
ESSENTIAL QUESTIONS:
A. Identify and classify triangles
by sides and by angles.
Review nightly homework
assignments.
• What is a triangle, and how are
they classified?
B. Apply the Angle Sum and the
Exterior Angle Theorems.
Monitor progress of students
during class.
(Formative Assessment)
• What is necessary to prove
congruence between two different
triangles?
C1. Name and label corresponding
parts of congruent triangles.
C2. Identify congruence
transformation.
Congruent Triangles
BIG IDEAS:
•
Triangles play a significant
role in geometry, so being
able to identify them is
D. Use the SSS, the SAS, the ASA,
and the AAS postulates and
theorems to test for triangle
congruence.
Short basic skills quiz.
Utilize constructions in class to
deepen the understanding of
congruent triangles.
In-class examples, practice, and
worksheets.
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Geometry
Content
essential.
• Proving triangles are
congruent involves the use
of theorems, properties, and
definitions.
• The understanding of
congruent parts of a triangle
is essential in proving
congruence.
Relationships in Triangles
Skills
E. Understand that Congruent Parts
of Congruent Triangles are
Congruent. (CPCTC).
F. Apply properties of isosceles
and equilateral triangles.
A. Identify and apply
perpendicular bisectors, angle
bisectors, altitudes, and medians in
triangles.
St. Mary's College High School
Assessment
(Formative Assessment)
Chapter 5 Test with multiple choice
and open-ended problems, twocolumn proofs, and critical thinking
problems. (Summative
Assessment)
Cumulative Final Exam on
chapters 1-5, with open-ended
problems, two-column proofs, and
critical thinking problems.
(Summative Assessment)
ESSENTIAL QUESTIONS:
•
•
B. Recognize and apply properties
of inequalities to the measure of
angles of a triangle, and to the
relationships between angles and
sides of a triangle.
What are bisectors,
medians, and altitudes, and
how are they determined?
How to determine if a figure
C. Use indirect proofs with Algebra
is a triangle.
and Geometry
BIG IDEAS:
•
•
Understand and be able to
find the bisectors, medians,
and altitudes of a triangle.
Application of each to
locate the centroid, the
circumcenter, and the
orthocenter of a triangle.
Content
D1. Apply the Triangle Inequality
Theorem.
D2. Determine the shortest
distance between a point and a line
in a coordinate plane.
E. Apply the SAS and the SSS
inequality theorems.
F. Practice problems for the entire
first trimester.
Skills
Assessment
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Geometry
St. Mary's College High School
Content
Proportions and Similarity
Skills
Assessment
ESSENTIAL QUESTIONS:
A1. Write and solve ratios.
A2. Solve proportions by using
cross products.
Review nightly assignments.
•
•
What is a proportion, and
how does it relate to
triangles?
What is similar, and how is
similat different from
congruent?
BIG IDEAS:
•
•
Understand how similar
triangles are in proportion.
Utilize this understranding
to solve problems involving
parts of triangles.
B. Identify similar polygons and
solve problems involving scale
factors.
C. Identify similar triangles, and
apply them to solve problems.
D. Divide segments into
proportional parts to determine
segment lengths.
Monitor progress of students
during class. Use of daily warm
ups, often in groups. (Formative
Assessments)
Assign Geometry Story to be
written, in order to introduce
students to upcoming Geometry
terms.
(Formative Assessment)
In-class examples, practice, and
worksheets.
(Formative assessment)
E. Recognize and apply
corresponding perimeters, altitudes,
angle bisectors, and medians of
Perform measuring activity
similar triangles to solve problems. demonstrating triangle similarity.
Right Triangles & Trigonometry
Weekly short basic skills quizzes.
ESSENTIAL QUESTION:
•
•
•
•
What is a right triangle, and
what special properties does
it have?
How is proportion related to
the geometric mean?
What is the Pythagorean
Thereom, and how is it
applicable to triangles?
What is trigonometry, and
how can it be used in real
life?
BIG IDEAS:
•
•
Understand and apply all
special properties of a right
triangle.
Understand the use of
trigonometry in the real
world.
A. Find the geometric mean
between two numbers, and apply
the relationship to parts of a right
triangle.
B. Use the Pythagorean Thereom
and its converse to find missing
sides of a triangle.
C. Use the properties of a 45-4590, and 30-60-90 right triangles.
D. Find trigonometric rations in
right triangles, and apply them to
solve problems.
Chapter 6 test, with several
multiple choice, open-ended and
critical thinking questions.
(Summative Assessment)
Use trigonmetric ratios to calculate
the height of various structures, or
trees.
(Formative Assessment)
Continued instruction with the
calculator, needed to determine trig
ratios.
Chapter 7 test, with open-ended,
and critical thinking problems.
(Summative Assessment)
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Geometry
Content
Quadrilaterals
ESSENTIAL QUESTIONS:
•
•
What are the various
quadrilaterals, and their
properties?
How are the properties
similar, and how are they
different?
BIG IDEAS:
•
Learn and understand the
various properties of each
quadrilateral.
Skills
A. Find the sum of the interior
and exterior angles of polygons.
B. Recognize and apply the
properties of the sides, angles, and
diagonals of parallelograms.
St. Mary's College High School
Assessment
Review nightly homework
assignments.
Monitor progress of students
during class. Use of daily warm
ups, often in groups.
(Formative Assessment)
Create quadrilateral family tree.
C. Recognize and apply the
properties of a rectangle, rhombus,
square, kite and trapezoid.
D. Graph vertices of
quadrilaterals on a coordinate
plane, and be able to identify them.
In-class examples, practice, and
worksheets.
(Formative Assessment)
Weekly short class basic skills
quizzes.
Chapter 8 test, with multiple
choice, open-ended and critical
thinking questions.
(Summative Assessment)
Content
Circles
Skills
Assessment
A. Find the sum of the intrerior
A1. Identify and use parts of
circles.
In-class examples, paractice and
warm up worksheets and activties.
Mainly group work. (Formative
Assessment)
ESSENTIAL QUESTIONS:
•
•
•
•
•
What is circumference?
What are central and
inscribed angles?
How are arcs measured?
What are tangents and
secants?
What is the equation for a
circle, and how can it be
graphed on a coordinate
plane?
BIG IDEAS:
•
•
Learn the components of a
circle, and what they mean.
Learn how to calculate arc
measures and arc lengths.
A2. Solve problems involving the
circumference of a circle.
B. Recognize major arcs, minor
arcs, central angles, inscribed
angles, and their measures.
Monitor progress of students
during class and homework review.
(Formative and Summative
Assessment)
Several short class quizzes on basic
skills material. (Summative
C. Use properties of tangents and
secants to solve problems involving Assessment).
circumscribed polygons.
Geometry Activity to create
D. Find measures of segments that understanding of circumference.
intersect in the interior and exterior
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Geometry
Content
• Know the difference
between a secant and a
tangent, and learn how to
use them to solve problems.
• Understand how to graph a
circle on a coordinate plane,
and be able to write the
equation for a circle.
Skills
of a circle.
Areas of Polygons and Circles
B. Find the area of triangles,
trapezoids, and rhombi.
•
What are the various
formulas used to determine
the area of polygons and
circles?
How can these formulas be
used to determine the area
of irregular figures?
Assessment
Chapter 10 Test with multiple
choice, open-ended, and critical
thinking questions. (Summative
Assessment)
A. Find the perimeters and ares
of parallelograms.
ESSENTIAL QUESTIONS:
•
St. Mary's College High School
C. Find the area of regulat
polygons and circles using the
apothem measurement.
Chapter 11 test, with multiple
choice, open-ended, and critical
thinking questions.
(Formative Assessment)
D. Learn to calculate the area of
irregular figurs by separating them
into triangles, trapezoids, rhombi,
or rectangles.
BIG IDEAS:
•
•
•
Learn all the formulas to
calculate the area of
pplygons and circles, and
how to apply them.
Review trigonometric
functions and the special
right triangle properties to
aid in the determination.
Use the radius to calculate
the area of circles.
Content
Surface Area:
Skills
Assessment
ESSENTIAL QUESTIONS:
A1. Use the orthogonal drawings
of three-dimensional figures to
make models.
A2. Identify and use threedimensional models.
In-class examples, practice, and
warm-up worksheets.
(Formative Assessment)
•
What are three dimensional
figures, and how can they
be sketched on paper?
Monitor progress of students during
class, and daily assignment review.
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Geometry
Content
•
•
What is a net, and how can
it be used to calculate the
surface area of various
shapes?
What are prisms, cylinders,
pyramids, cones, and
spheres, and how are their
surface areas calculated?
Skills
B. Draw two-dimensional
modesl for three-dimensional
figures, and calculate the surface
area of the figures.
C. Find the lateral areas and the
total surface areas of prisms.
D. Find the lateral areas and the
total surface areas of cylinders.
BIG IDEAS:
•
•
Learn how to sketch threedimensional on special
orthogonal paper.
Learn the formulas for the
surface areas of prisms,
cylinders, pyramids, cones,
spheres, & how to apply
them.
E. Find the lateral areas and the
total surface areas of regular
pyramids.
F. Find the lateral areas and the
total surface areas of cones.
St. Mary's College High School
Assessment
(Formative Assessment)
Weekly short quizzes.
Demonstrations of prisms,
cylinders, pyramids, and cones in
class.
Chapter 11 Test, with open-ended
and critical thinking problems.
(Summative Assessment)
Cumulative Final Exam for
chapters 6-11, with multiple choice,
open-ended, word problems, and
critical thinking questions.
(Summative Assessment)
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