DEPARTMENT: Mathematics DATE: 2007-2008

COURSE TITLE: Geometry Honors COURSE NUMBER: 5230

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YEAR
QPA: 5.0

o SEMESTER CREDITS: 5

TEXTBOOK: (Title, Author, Publisher, Edition)

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

MATERIALS USED:TI-84 Plus graphing calculators, IBM ThinkPad, supplementarymaterials 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 Geometry1. 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 Proof1. The role of reasoning in geometry

2. Comparing and contrasting inductive reasoning and deductive reasoning

3. Learning the importance of counterexamples in disproving

statements4. 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 Lines1. Identifying angles formed when a pair of lines is intersected by a

third line2. 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 Triangles1. 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

congruent5. Equilateral and isosceles triangles

6. Relating congruence to transformation

Unit 5: Relationships within Triangles1. 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 proportions2. Writing proportions to solve real-life application problems

3. Calculating the geometric mean between a pair of numbers

SECOND SEMESTER

Unit 6: Similarity1. 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 Trigonometry1. 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 polygons2. Properties of parallelograms

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

kites4. Special quadrilaterals

Unit 10: Properties of Circles1. 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 Area1. Areas of triangles, parallelograms, rectangles, rhombuses, and

kites2. 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 Solids1. Finding the surface area of prisms, cylinders, pyramids and

cones2. Calculating volumes of pyramids, cones, prisms, and cylinders

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