Geometry B 2003-04

Geometry – Holt, Rinehart & Winston

Grades 10-11

Mr. Collyard

Course Purpose: Geometry is a course in which God’s gift of mathematics is used to deepen the student’s understanding and respect for His creation.

Course Goal: To connect the fundamentals of arithmetic and algebra to the physical world using geometric models and concepts so that students will be able to use this understanding to discover and make mathematical applications they will meet in the world in which God has placed us.

Course Outcomes: The student will…

learn to appreciate geometry as a gift from God enabling the student to understand and respect His creation.
develop personal understanding and definitions of geometric terms.
develop a connection between geometric models and the real world.
use this understanding and these definitions combined with logical thinking to discover mathematical properties.

Unit Outcomes:

Chapter 1: Exploring Geometry pp. 2-77

The students will…

· begin to construct a geometry portfolio that will help them to organize their work.

· define segment, ray, angle, collinear, intersect, intersection, and coplanar.

· investigate postulates about points, lines, and planes.

· construct a geometry ruler.

· define length and congruent.

· identify and use the Segment Addition Postulate.

· measure angles with a protractor.

· identify and use the Angle Addition Postulate.

· use paper folding to construct perpendicular lines, parallel lines, segment bisectors, and angle bisectors.

· define and make geometry conjectures.

· discover points of concurrency in triangles.

· draw the inscribed and circumscribed circles of triangles.

· identify and draw the three basic rigid transformations: translation, rotation, and reflection.

· review algebraic concepts of coordinate plane, origin, x-and y-coordinates, and ordered pair.

· construct translations, reflections across axes, and rotations about the origin on a coordinate plane.

Chapter 2: Reasoning in Geometry pp. 78-135

The students will…

· investigate some interesting proofs of mathematical claims.

· understand the meaning of the term proof.

· use conditionals in logical arguments.

· form the converses of conditionals.

· create logical chains from conditionals use Euler diagrams to study definitions of objects.

· use principles of logic to create definitions of objects.

· identify and use the Equivalence Properties of Equality and Congruence.

· link the steps of a proof by using properties and postulates.

· develop theorems from conjectures.

· write two-column proofs.

Chapter 3: Parallels and Polygons pp. 136-207

The students will…

· define polygon.

· define and use reflectional symmetry and rotational symmetry.

· define regular polygon, center of a regular polygon, central angle of a regular polygon, and axis of symmetry.

· define quadrilateral, parallelogram, rhombus, square, and trapezoid.

· identify properties of quadrilaterals and the relationship among the properties.

· define transversal, alternate interior angles, alternate exterior angles, same-side interior angles, and corresponding angles.

· make conjectures and prove theorems by using postulates and properties of parallel lines and transversals.

· identify and use the converse of the Corresponding Angles Postulate.

· prove that lines are parallel by using theorems and postulates.

· identify and use the Parallel Postulate and the Triangle Sum Theorem.

· define interior and exterior angles of a polygon.

· develop and use formulas for the sums of the measures of interior and exterior angles of a polygon.

· define midsegment of a triangle and midsegment of a trapezoid.

· develop and use formulas based on the properties of triangle and trapezoid midsegments.

· develop and use theorems about equal slopes of perpendicular lines.

· solve problems involving perpendicular and parallel lines in the coordinate plane by using appropriate theorems.

Chapter 4: Congruence pp. 208-291

The students will…

· define congruent polygons.

· solve problems by using congruent polygons.

· explore triangle rigidity.

· develop three congruence postulates for triangles – SSS, SAS, ASA.

· use counter examples to prove that the other side and angle combinations cannot be used to prove triangle congruence.

· use congruence of triangles to conclude congruence of corresponding parts.

· develop and use the Isosceles Triangle Theorem.

· prove quadrilateral conjectures by using triangle congruence postulates and theorems.

· develop conjectures about special quadrilaterals – parallelograms, rectangles, and rhombuses.

· construct congruent copies of segments, angles, and triangles.

· construct an angle bisector.

· translate, rotate, and reflect figures by using a compass and straightedge.

· prove that translations, rotations, and reflections preserve congruence and other properties.

· use the Betweeness Postulate to establish the Triangle Equality Theorem.

Chapter 5: Perimeter and Area pp. 292-369

The students will…

· identify and use the Area of a Rectangle and Sum of Areas Postulates.

· solve problems involving fixed perimeters and fixed areas.

· develop area formulas of triangles, parallelograms, and trapezoids.

· solve problems by using formulas for the areas of triangles, parallelograms, and trapezoids.

· identify and apply formulas for the circumference and area of a circle.

· solve problems by using formulas for the circumference and are of a circle.

· identify the Pythagorean Theorem and its converse.

· solve problems by using the Pythagorean Theorem.

· identify and use the45-45-90 Triangle Theorem and the 30-60-90 Triangle Theorem.

· develop and apply the distance formula.

· use the distance formula to develop techniques for estimate the area under a curve.

· develop coordinate proofs for the Triangle Midsegment Theorem, the diagonals of a parallelogram, and the reflection for a point across a line.

· use the concepts of coordinate proofs to solve problems on the coordinate plane.

· develop and apply the basic formula for geometric probability.

Chapter 6: Shapes in Space pp. 370-427

The students will…

· use isometric dot paper to draw three-dimensional shapes built with cubes.

· develop an understanding of orthographic projection.

· develop a basic understanding of volume and surface area.

· define polyhedron.

· identify the relationships of points, lines, segments, planes, and angles in three-dimensional space.

· define dihedral angle.

· define prism, right prism, and oblique prism.

· examine the shapes of lateral faces of prisms.

· solve problems by using the diagonal measure of a right prism.

· identify the features of a three-dimensional coordinate system, including axes, octants, and coordinate planes.

· solve problems by using the distance formula in three dimensions.

· define the equation of a line and the equation of a plane in space.

· solve problems by using the equation of a line and the equation of a plane in space.

· identify and define the basic concepts of perspective drawing.

· apply these basic concepts to creating your own perspective drawings.

Chapter 7: Surface Area and Volume pp. 428-495

The students will…

· explore ratios of surface area to volume

· develop the concepts of maximizing volume and minimizing area.

· define and use the formula for finding the surface area of a right prism.

· use Cavalieri’s Principle to develop the formula for the volume of a right or oblique prism.

· define and use the formula for the surface area and volume of a pyramid.

· define and use the formula for the surface area and volume of a right cylinder.

· define and use the formula for the surface area and volume of a cone.

· define and use the formula for the surface area and volume of a sphere.

· define various transformations in three-dimensional space.

· solve problems by using transformations in three-dimensional space.

Chapter 8: Similar Shapes pp. 496-561

The students will…

· construct the dilation of a segment and a point by using a scale factor.

· construct a dilation of a closed plane figure.

· use properties of proportions and scale factors to solve problems involving similar polygons.

· develop the AA Triangle Similarity Postulate and the SSS and SAS Triangle Similarity Theorems.

· develop and prove the Side-Splitting Theorem.

· use the Side-Splitting Theorem to solve problems.

· use triangle similarity to measure distances indirectly.

· develop and use similarity theorems for altitudes and medians of triangles.

· develop and use ratios for areas of similar figures.

· develop and use ratios for volume of similar solids.

· explore relationships between cross-sectional area, weight, and height.

Chapter 9: Circles pp. 562-627

The students will…

· define circle and its associated parts, and use them in constructions.

· define and use the degree measure of arcs.

· define and use the length measure of arcs.

· prove a theorem about chords and their intercepted arcs.

· define tangents and secants of circles.

· understand the relationship between tangents and certain radii of circles.

· understand the geometry of a radius perpendicular to a chord of a circle.

· define inscribed angle and intercepted arc.

· develop and use the Inscribed Angle Theorem and its corollaries.

· define angles formed by secants and tangents of circles.

· develop and use theorems about measures of arcs intercepted by these angles.

· define special cases of segments related to circles, including secant-secant, secant-tangent, and chord-chord.

· Develop and use the theorems about measures of the segments.

· Develop and use the equation of a circle.

· adjust the equation for a circle to move the center in a coordinate plane.

Chapter 10: Trigonometry pp. 628-695

The students will…

· define the tangent ratio by using right triangles.

· use a chart or graph to find the tangent of an angle or the angle for a given tangent.

· solve problems using tangent ratios.

· explore the relationship between the measure of an angle and its sine and cosine.

· solve problems by using sine and cosine ratios.

· develop two trigonometric identities.

· use a rotating ray on a coordinate plane to define angles measuring greater than 90° and less than 0°.

· Define sine, cosine, and tangent for angles of any size.

· develop the law of sines.

· use the law of sines to solve triangles.

· use the law of cosines together with the law of sines to solve triangles.

Instructional Strategies

Lecture/Discussion(30%) Student Discovery with Manipulatives(20%) Active Practice(30%) Cooperative Group Work(20%)

Grading

Daily assignments will be given each day. These assignments become the basic learning tool. Assignments completed thoroughly are the key to your success. Assignments should be kept in a required 3-ring binder. Daily assignment grading will be based on neatness, thoroughness, and timeliness. Basically, if you do your work as indicated, your daily grade will be an A. Daily work counts the equivalent of one major test.
Worksheets that review material that has been taught and previously practiced will be given periodically to check understanding. These will be graded and count 1/3 as much as a test.
Quizzes/Tests: Quizzes will be used to check understanding at regular intervals in each chapter(c. 25% of your quarter grade). Chapter tests will be used to determine mastery of material(c. 50% of your quarter grade)
Special projects, reports, journal writing, and a portfolio will be used as additional assessment tools.
Semester Exam: At the end of each semester a major exam will be taken. The exam grade will be part of the semester grade and will count no more than 20% of the semester grade.

Student Materials

Ö TI-83 Plus Calculator(TI-83 acceptable)

Ö Pencil, 3-hole paper, textbook

Ö 3-ring binder

Ö straight edge, compass, protractor

Ö scissors(optional)

Classroom Procedures

· Respect classmates and teachers.

· Do not bring food or drinks into the classroom.

· Bring proper supplies to class.

· Complete all assignments thoroughly and on time.

· Be an active learner by being a good listener, participating in class activities, and speaking only with permission.

· When you are absent, see the teacher the first day you are back for make-up work.

“Excel through Christ”

“I can do everything through him who gives me strength.” Phil. 4:13