**
DEPARTMENT:
Mathematics
DATE: 2007-2008**

**
COURSE TITLE:
Geometry
COURSE NUMBER: 5210**

**o
YEAR
QPA: 4.5**

**
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, protractor
and compass**

**GOALS:
**

**1.**
**To provide a basic comprehensive course in geometry that is very concrete
and visual.**

**2.**
**To discern patterns and recognize properties of two-dimensional geometric
shapes.**

**3.**
**To reinforce the fundamentals of algebra in a geometric setting.**

**4.**
**To prepare students for the Math portions of the SAT.**

**5.**
**To use visualization, spatial reasoning, and geometric modeling to solve
pro-blems.**

**6.**
**To use graphing calculators and measurement tools to analyze, solve,
visualize, and clarify geometric concepts.**

** **

** **

**CONTENT OF COURSE:**

** **

**FIRST SEMESTER**

** **

**Unit 1: Fundamentals of Geometry**

**1.**
**Naming points, lines, rays, line segments and planes**

**2.**
**Segment addition and congruence**

**3.**
**Finding the midpoint and length of a line segment on a coordinate plane**

**4.**
**Measuring and classifying angles**

**5.**
**Angle addition**

**6.**
**Special angle pair relationships**

**7.**
**Classifying polygons**

**8.**
**Perimeter, circumference, and area measurements**

**Unit 2: Reasoning and Proof**

**1.**
**Using inductive reasoning to arrive at conjectures about observed events**

**2.**
**Testing the validity of conjectures**

**3.**
**Converting factual statements into conditional statements**

**4.**
**Writing the converse of conditional statements**

**5.**
**Point, line, and plane postulates**

**6.**
**Review algebraic properties of equality**

**7.**
**Right Angle Congruence Theorem**

**8.**
**Linear Pair Postulate**

**9.**
**Vertical Angles Congruence Theorem**

**Unit 3: Parallel and Perpendicular Lines**

**Review the concepts of parallel and perpendicular lines and planes****Skew lines****Special angle pairs formed when a transversal intersects a pair of lines****Measurements of special angle pairs formed when the lines intersected by a transversal are parallel****Review of slopes of lines****Review of writing and graphing equations of lines****Perpendicular transversal theorem**

** **

**SECOND SEMESTER**

** **

**Unit 4: Congruent Triangles**

**1.**
**Classification of triangles by side lengths**

**2.**
**Classification of triangles by angle measurements**

**3.**
**Triangle Sum Theorem**

**4.**
**Exterior Angle Theorem**

**5.**
**Properties of congruent figures**

**6.**
**Prove triangles are congruent by SSS, SAS, ASA, and AAS**

**7.**
**Real life applications of triangle congruence**

**8.**
**Isosceles and equilateral triangles**

**9.**
**Congruence transformations**

**Unit 5: Relationships within Triangles**

**1.**
**Midsegment Theorem**

**2.**
**Perpendicular bisectors**

**3.**
**Angle bisectors**

**4.**
**Medians**

**5.**
**Altitudes**

**6.**
**Relationship between side length and angle measurement in a triangle**

**7.**
**Triangle Inequality Theorem**

**Unit 6: Similarity**

**1.**
**Ratios**

**2.**
**Proportions**

**3.**
**Geometric mean**

**4.**
**Using proportions to solve problems**

**5.**
**Similar polygons**

**Unit 7: Right Triangles**

**1.**
**Pythagorean Theorem**

**2.**
**Pythagorean triples**

**3.**
**Converse of Pythagorean Theorem**

**4.**
**Special right triangles**

**
**

** **

**Students will be able to…**

** **

**Unit 1: Fundamentals of Geometry**

**Identify points, lines, line segments, rays and planes.****Symbolically name a point, a line, a line segment, a ray and a plane.****Recognize problematic situations that call for segment addition.****Calculate the midpoint and length of a line segment.****Identify segment congruence.****Name, measure, and classify angles.****Recognize problematic situations that call for angle addition.****Identify special angle pairs: complementary, supplementary, linear pair and vertical angles.****Classify polygons.****Find the area and perimeter of rectangles and triangles.****Find the circumference and area of circles.**

** **

**Unit 2: Reasoning and Proof**

**Use inductive reasoning to form conjectures about observed events.****Determine the validity of a conjecture and present a counterexample to demon-strate the falsity of an invalid conjecture.****Convert a factual statement into a conditional statement.****Identify the hypothesis and conclusion of a conditional statement.****Write the converse of a conditional statement.****Interpret geometric diagrams by means of point, line, and plane postulates.****Appreciate that algebraic properties of equality substantiate all of the steps used to solve an algebraic equation.****Understand that all right angles are congruent.****Understand that angles that form a linear pair are supplementary.****Understand that vertical angles are congruent.**

**Unit 3: Parallel and Perpendicular Lines**

**Recognize parallel, perpendicular and skew lines and understand the distinctions between them.****Distinguish between corresponding, alternate interior, alternate exterior and con-secutive interior angles formed when a transversal intersects a pair of lines.****Determine the measurements of all eight angles formed when a pair of parallel lines are intersected by a transversal when only one of the angle measurements is known.****Determine the slope of a line when viewing its graph.****Calculate the slope of a line algebraically by means of the slope formula.****Write the equation of a line when presented with its graph.****Appreciate that the perpendicular transversal theorem is an extension of angle re-lationships present when a pair of parallel lines are intersected by a transversal.**

** **

**Unit 4: Congruent Triangles**

**1.**
**Distinguish between scalene, isosceles, and equilateral triangles.**

**2.**
**Distinguish between acute, right, obtuse, and equiangular triangles.**

**3.**
**Determine the measurement of a missing angle of a triangle by means of
the Triangle Sum Theorem.**

**4.**
**Understand how the measurement of an exterior angle of a triangle relates
to the measurements of its interior angles.**

**5.**
**Identify all pairs of congruent corresponding parts of congruent figures.**

**6.**
**Determine if figures are congruent.**

**7.**
**Appreciate that congruent triangles can be used to find distances that
are difficult to measure directly.**

**8.**
**Create an image congruent to a given figure in the coordinate plane.**

**9.**
**Distinguish between the three main types of transformations.**

**Unit 5: Relationships within Triangles**

**1.**
**Identify special triangle segments.**

**2.**
**Use the Midsegment Theorem to find lengths within a triangle.**

**3.**
**Understand the properties of points located on perpendicular or angle
bisectors.**

**4.**
**Explain how triangle side lengths relate to angle measurements.**

**5.**
**List the sides of a triangle in order when given its angle measurements
and vice versa.**

**6.**
**List possible lengths of the third side of a triangle when the lengths of
its two other sides are given.**

** **

**Unit 6: Similarity**

**1.**
**Simplify a ratio.**

**2.**
**Use ratios to find missing dimensions.**

**3.**
**Recognize a proportion and use the cross products property to solve it.**

**4.**
**Recognize when a proportion approach is appropriate for solving real
world pro-blems.**

**5.**
**Calculate the geometric mean of two numbers and present it in simplest
radical form.**

**6.**
**Identify similar polygons by investigating angle measurements and
proportional-ity of corresponding sides.**

**7.**
**Determine the scale factor of similar polygons and use it to determine
lengths of missing dimensions.**

**8.**
**Appreciate that similar polygons also exhibit proportionality of
perimeters and in-ternal segment lengths.**

**Unit 7: Right Triangles**

**1.**
**Apply the Pythagorean Theorem to determine the length of a missing side
of a right triangle.**

**2.**
**Recognize common Pythagorean triples and their multiples.**

**3.**
**Understand that these Pythagorean triples can be put to use to quickly
arrive at the length of a missing side of a right triangle.**

**4.**
**Use the Pythagorean Theorem to classify a triangle as right, acute, or
obtuse.**

**5.**
**Understand the relationship between side lengths in 45-45-90 and 30-60-90
trian-gles.**

**6.**
**Quickly present the length in simplest radical form of a missing side in
45-45-90 and 30-60-90 by means of these relationships.**