Download Advanced Geo course outline

Geometry Advanced
Anticipated Course Outline
Ms. Heyl
This is for you and your parents. It is very helpful to keep up with what topics I am teaching. If
you have any trouble, you can use these key words to search for help on the websites I will be
providing you all with. Listed next to each topic is the section from which you can find this
information in your textbook. I plan on spending about one or two days on each topic,
depending on the student’s understanding. Quizzes will be administered on occasion, and tests
will be given at the end of each unit, with at LEAST four days’ notice.
Student will be able to:
Textbook
Unit 1: Elements of Geometry
1.
2.
3.
4.
5.
6.
7.
8.
1.2
1.2, 3.1,
1.3, 1.7, 5.2,
3.1
3.2
3.3
3.4
3.5
1.3,
Supplemental
Material
1.5
1.2
1.1, 11.1, 11.2
1.6
9.
10.
11.
12.
13.
Define Points, Lines and Planes
Define and distinguish Collinearity/Coplanar
Understand Betweenness/ Distance in line segments
Identify relationships between figures in space
Prove Theorems about Parallel Lines
Determine whether two lines are parallel
Relate Parallel and Perpendicular Lines
Use Parallel lines to prove a theorem about triangles
Bisect/Trisect line segments
Know when to make Assumptions from Diagrams
Understand Definitions/Postulates/Theorems
Understand Dimensions
Make basic constructions using a straight edge and
compass
14. Construct Parallel and Perpendicular Lines
3.6
Added information to Unit 1: Coordinate Geometry
Student will be able to:
1.
2.
3.
4.
5.
6.
To Apply Coordinate Geometry
Find the Midpoint of a segment in the Coordinate Plane
Find the Distance between any two points in the Coordinate Plane
Write and graph linear equations using Slope
Relate Slope to Parallel and Perpendicular Lines
Find Perimeter/Area of Figures in the Coordinate Plane
6.8
1.7
1.7
3.7
3.8
1.8
Unit 2: Angles
Student will be able to:
1.
2.
3.
4.
5.
Define and Identify Vertical Angles
Define and calculate Complementary/Supplementary angles
Classify Angles (obtuse, acute, right)
Work With angles formed by Parallel Lines
Use the Perpendicular Angle Bisector Theorem
1.5
1.5
1.4
3.1
5.2
Student will be able to:
1. Find the Sums of Angles in triangles
2. Classify triangles by Angles and Sides
3. Find Relationships between angles and sides
Instructional
Resources for
CP Geometry :
Geometry
Foundations
Series,
(Prentice Hall)
Unit 3: Triangles
3.5
6.7, 8.1
5.6
4. Understand and use theTriangle Inequality Theorem in one and
two triangles
5. Review: Simplify square roots
6. Use the Right Triangle/Pythagorean Theorem
7. Use Properties of Perpendicular Bisectors and Angle Bisectors
8. Identify properties of perpendicular bisectors and angle bisectors
9. Recognize Congruent Figures and their Corresponding Parts
10. Prove Triangles Congruent using SSS, SAS, ASA, AAS,
11. Use corresponding parts of Congruent Triangles
12. Use properties of Isosceles & Equilateral Triangles to solve
problems
13. Review: To solve systems of equations
5.6, 5.7
6.7
8.1
5.2
5.3
4.1
4.2, 4.3, 4.4
4.4
4.5
4.6
4.6
14. Prove Right Triangles Congruent using HL
4.7
15. Identify Congruent Overlapping Triangles
16. Prove two triangles congruent using other congruent triangles
4.7
Added information to Unit 3: Triangles
Instructional
Resources for
CP Geometry :
Geometry
Foundations
Series,
(Prentice Hall)
Student will be able to:
1. To use the properties of special right triangles: 45-45-60 and
30-60-90
2. Use and Apply Right Triangle Trigonometry
3. Use and Apply Related Triangle Theorems
4. Use the Law of Sines and Law of Cosines
Unit 4: Transformations
8.2
8.3, 8.4
8.4
8.5,8.6
Instructional
Resources for
CP Geometry :
Geometry
Foundations
Series,
(Prentice Hall)
Student will be able to:
1. Define Congruency of figures
2. Translate, Rotate, Reflect figures
3. To find composition of isometries, including glide reflections.
4. To classify isometries.
5. To identify and prove triangle congruence using isometries.
5. To understand dilation images of figures.
6. To identify similarity transformations and
verify properties
of similarity.
4.1
9.1, 9.2, 9.3
9.4
9.4
9.5
9.6
9.7
Unit 5: Similarity
Student will be able to:
1. Write Ratios and Solve Porportions
2. Identify and apply similar polygons
7.1
7.2
7.3
3. Use the AA~ Postulate and the SAS~ and SSS~ Theorems
7.3
4. Use similarity to find indirect measures
7.4
5. Find and use relationships in similar right triangles
7.5
6. Use the Side Splitter Theorem and Triangle-Angle-Bisector Theorem
Unit 6: Area and Perimeter
Instructional
Resources for
CP Geometry :
Geometry
Foundations
Series,
(Prentice Hall)
Student will be able to:
1.
2.
3.
4.
Find the areas of parallelograms and trianges
Find the area of a trapezoid, rhombus, or kite
Find the area of a regular polygon
Find the areas of triangles and regular polygons using
trigonometry
5. Use the Law of Sines and Trigonometric ratios to derive
A
1
abSinC . Apply this formula.
2
6. Find Perimeter/Area of figures in the Coordinate plane
7. Find theoretical probability and geometric probability
1.8, 10.1
10.2
10.3
10.5
8.5,8.6, 10.5
1.8, supplemental
material
10.8
Unit 7: 3-D Figures
Student will be able to:
1. Recognize Polyhedra and their parts and visualize cross sections of
space figures
11.1
11.2
2. Find the Surface Area of a Prism and Cylinder
11.3
3. Find the Surface Area of a Pyramid and Cone
4. Find the volumes of prisms and cylinders
5. Find the volumes of pyramids and cones
11.4
11.5
11.6
6. Find the surface are and volume of a sphere
11.7
7.
8.
9.
10.
11.
Compare and find areas and volumes of similar solids
Draw Nets of Polyhedra
Draw Perspective Drawings and Views
Translate from 2D to 3D
Demonstrate Modeling
1.1
11.1 extension
1.1
1.8, 11.3, 11.5, 11.6
Unit 8: Quadrilaterals
Student will be able to:
1. Identify Quadrilaterals
1.8
2. Find the Measure of Interior and Exterior Angles of Polygons
6.1
3. Find and use Relationships between sides and angles of
parallelograms
6.2
4. Determine Whether a quadrilateral is a parallelogram
6.3
5. Define and Classify Special Types of Parallelograms
6.4
6. Use Properties of Diagonals in Rectangles and Rhombuses
6.4
7. Determine whether a Parallelogram is a Rectangle or a Rhombus
6.5
8. Verify and use Properties of Trapezoids and Kites
6.6
9. Classify Polygons in the Coordinate Plane
6.7
10. Name coordinates of special figures
6.8
1. Find the sum and measures of interior and exterior angles of
n-sided polygons
6.1
2. Name/Classify polygons
1.8 Review
Unit 9: Circles
Student will be able to:
1. Find measures of Angles formed by Tangents, Chords, and Secants
2. Use Congruent Chords, Angles and Arcs
3.
4.
5.
6.
7.
8.
9.
10.
11.
Find the measure of central angles and arcs.
Find the areas of circles, sectors and segments of circles
Find Circumference of Circles
Find the Measure of Inscribed Angles
Identify Circumscribed Figures/Circles
Use Properties of Tangent Lines
Write the equation of a circle
Find the Center and Radius of a Circle
To draw and describe a locus
Unit 10: Proofs
12.4
12.2
10.6
10.7
1.8
12.3,
5.3, 12.1
12.1
12.5
12.5
12.6
1.
2.
3.
4.
5.
6.
7.
8.
9.
Use Inductive Resoning to Make Conjectures
Use theTransitive Property
UseParagraph/Indirect Proofs
Write Conditional Statements and their Parts
Write converses, inverses, and Contrapositives of
Conditionals
Write Biconditionals and Recognize Good Definitions
Use Deductive Resoning in Proofs
Connect Reasoning in Algebra and Geometry
Prove and Apply Theorems about Angles
Instructional
Resources for
CP Geometry :
Geometry
Foundations
Series,
(Prentice Hall)
Student will be able to:
2.1
2.5
5.5
2.2
2.2
2.3
2.4
2.5
2.6