Geometry Honors: Goals and Course Outline

 

 

DEPARTMENT: Mathematics                                         DATE: 2007-2008

COURSE TITLE: Geometry Honors                               COURSE NUMBER:  5230

o YEAR                                                                    QPA: 5.0

o SEMESTER                                                           CREDITS: 5

 

 

TEXTBOOK: (Title, Author, Publisher, Edition)

McDougal Littell Geometry (Both print and electronic editions), Larson, Boswell, Kanold, & Stiff, McDougal Littell Inc., 2007

 

MATERIALS USED:  TI-84 Plus graphing calculators, IBM ThinkPad, supplementary

      materials as supplied by McDougal Littell

 

GOALS:  

1.      To provide an honors level course for students who aspire to an advanced level of learning.

2.      To develop geometric skills and concepts and apply them to real-life applications.

3.  To develop the ability to construct formal logical arguments and proofs in a geometric setting.

4.   To provide students with experiences that deepen the understanding of two- and three-dimensional objects and their properties.

5.      To prepare students for the Math portions of the SAT.

6.      To use technology and geometric measurement to explore concepts and applications  of geometry.

 

CONTENT OF COURSE:

 

FIRST SEMESTER

 

Unit 1: Essentials of Geometry

1.      Identifying and naming points, lines, planes, and rays

2.      Comparing line segments and identifying congruent segments

3.      Segment Addition Postulate

4.      Distance formula and midpoint formula

5.      Classifying angles

6.      Angle Addition Postulate

7.      Special angle relationships

8.      Polygons

9.      Perimeter, circumference, and area measurements

 

Unit 2: Reasoning and Proof

1.      The role of reasoning in geometry

2.      Comparing and contrasting inductive reasoning and deductive reasoning

3.      Learning the importance of counterexamples in disproving  
 statements

4.      Analyzing conditional statements and identifying the hypothesis and conclusion

5.      Writing converse, inverse, and contrapositive statements and assessing their validity

6.      Reasoning using properties from algebra

7.      Using postulates and theorems in writing two-column proofs

 

Unit 3: Parallel and Perpendicular Lines

1.      Identifying angles formed when a pair of lines is intersected by a
 third line

2.      Using parallel lines and transversals to determine angle measurements

3.      Proving lines are parallel and perpendicular

4.      Using coordinate geometry to find slopes, parallel lines,
 perpendicular lines, and equations of lines

      5.  Writing and graphing equations of lines

 

Unit 4:  Congruent Triangles

1.      Classifying triangles and determining angle measurements

2.      Properties of congruent figures

3.      Using SSS, SAS, HL, ASA, and AAS to prove triangles are congruent

4.      Using congruent triangles to prove corresponding parts are
 congruent

5.      Equilateral and isosceles triangles

6.      Relating congruence to transformation

 

Unit 5:  Relationships within Triangles

1.      Midsegments of triangles

2.      Perpendicular bisectors and angle bisectors of triangles

3.      Medians and altitudes of triangles

4.      Comparing the lengths of the sides or the measures of the
angles of triangles

 

Unit 6:  Similarity

       1.  Reciprocal and cross product properties of proportions

      2.  Writing proportions to solve real-life application problems

      3.  Calculating the geometric mean between a pair of numbers

 

 

SECOND SEMESTER

 

Unit 6: Similarity

1.      Identifying similar polygons and triangles

2.      AA Similarity Postulate, SSS and SAS Similarity Theorems

3.   Using similar triangles and proportionality theorems to solve real-life problems

4.    Analysis of similar triangles formed within a right triangle when an altitude has been drawn to the hypotenuse of the right triangle

 

Unit 7:  Right Triangles and Trigonometry

1.      The Pythagorean Theorem

2.      The converse of the Pythagorean Theorem

3. Properties of special right triangles (30-60-90 and 45-45-90 triangles)

4.    Trigonometric ratios of an acute angle and their use to solve right triangle problems in real-life applications

5. Use of Law of Sines and Cosines

 

Unit 8:  Quadrilaterals

    1. Interior and exterior angle measures of polygons

   2. Properties of parallelograms

   3. Properties of rhombuses, rectangles, squares, trapezoids and
       kites

   4. Special quadrilaterals

 

Unit 10:  Properties of Circles

    1.   Tangents, chords, and secants of circles

    2.   Properties of chords, inscribed angles, and inscribed polygons

    3.   Arc measures and segment lengths in circles

    4.   Writing and graphing equations of circles

 

Unit 11:  Measuring Length and Area

      1.  Areas of triangles, parallelograms, rectangles, rhombuses, and 
           kites

      2.  Area and circumference of a circle

      3.  Arc lengths and areas of sectors in a circle

      4.  Areas and perimeters of regular polygons

      5.  Geometric probability

 

Unit 12:  Surface Area and Volume of Solids

      1.  Finding the surface area of prisms, cylinders, pyramids and
           cones

      2.  Calculating volumes of pyramids, cones, prisms, and cylinders

 

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