COURSE TITLE: Geometry 0520
COURSE DESCRIPTION: Geometry stresses discovery and problem-solving and applies deductive structure of proofs to proving congruent and similar triangles. Topics covered include lines and their subsets, angles, triangles, congruence, similarity, inequalities, parallel and perpendicular lines, polygons and quadrilaterals, area, circles and right triangle trigonometry.
Prerequisite: Placement by the Mathematics Department and completion of Algebra I or Algebra, Part II.
COURSE REQUIREMENTS/REQUIRED MATERIALS:
1. Text: Geometry: Glencoe, McGraw-Hill, copyright 2008.
2. Pencils.
3. Five subject spiral notebook.
4. Scientific calculator.
COURSE OBJECTIVES/STUDENT OUTCOMES:
1) Students will become familiar with the language of geometry.
Upon completing this goal, the student will be able to
• graph ordered pairs on a coordinate plane
• identify collinear and coplanar points and intersecting lines and planes
• find the distance between points on a number line,
find the distance between points in the coordinate plane
• find the midpoint of a segment
• identify angles and parts of angles
• classify angles as acute, obtuse, right and straight
• identify and use adjacent angles, vertical angles,
complementary angles, supplementary angles,
and linear pairs of angles.
2) Students will experience the elements of deductive reasoning.
Upon completing this goal the student will be able to:
• identify the hypothesis and conclusion of an if-then statement
• write the converse of an if-then statement
• identify and use basic postulates about points, lines, and planes
• use the laws of deductive reasoning
• properly write a proof
3) Students will develop an understanding of the relationship between
angles formed by a transversal intersection parallel line.
Upon completing this goal the student will be able to:
• identify the relationships between pairs of angles formed
by pairs of lines and transversals
• recognize angle conditions that produce parallel lines
• prove two lines are parallel based on given angle relationships
• find the slope of a line
• use slope to identify parallel and perpendicular lines
4) Students will acquire an understanding of congruent triangles
and their corresponding parts.
Upon completing this goal the student will be able to:
• identify the parts of a triangle
• classify triangles
• identify congruent triangles
• name and label corresponding parts of congruent triangles
• use postulates SSS, etc. to test for triangle congruence
5) Students will recognize the applications of congruent triangles.
Upon completing this goal the student will be able to:
• identify and use medians, altitudes, angle bisectors
and perpendicular bisectors in a triangle
• recognize and apply relationships between the sides
and angles in a triangle
6) Students will gain an understanding of the properties of
quadrilaterals and the relationship that exists between
quadrilaterals.
Upon completing this goal the student will be able to:
• recognize and define a parallelogram
• use the properties of a parallelogram
• recognize and define a rectangle
• use the properties of a rectangle
• recognize and define the properties of squares and rhombi
• use the properties of squares and rhombi
• recognize and define the properties of trapezoids
• use the properties of trapezoids
7) Students will develop a familiarity with the properties
and applications of similarity.
Upon completing this goal the student will be able to:
• recognize and use ratios and proportions
• identify similar figures
• solve problems involving similar figures
8) Students will experience an introduction to
right triangle trigonometry.
Upon completing this goal the student will be able to:
• find the geometric mean between two numbers
• use the Pythagorean theorem
• recognize and use trigonometric relationships from right triangles
• solve triangles using the law of sines and the law of cosines
9) Students will gain familiarity with the properties of a circle
and the relationship of circles to special lines, i.e. chords,
secants, tangents.
Upon completing this goal the student will be able to:
• name parts of a circle
• write an equation of a circle in the plane
• recognize major and minor arcs of circles
• find the measures of arcs and central angles
• find the measures of inscribed angles
• find the measures of angles formed by intersecting
chords, secants and tangents in relation to intercepted arcs
• find the measures of segments formed by intersecting
chords, secants and tangents in relation to intercepted arcs
10) Students will develop a conceptual understanding
of the area of a plane figure.
Upon completing this goal the student will be able to:
• identify and name polygons
• identify faces, edges and vertices of a polyhedron
• find the sum of the measures of the interior and
exterior angles of a convex polygon
• find the measure of each interior and exterior
angle of a regular polygon
• find the area of all standard quadrilaterals
• find the area of regular polygons
• find the area of a circle
11) Students will acquire an understanding of the surface area
and volume of three dimensional figures
Upon completing this goal the student will be able to:
• draw three dimensional figures
• identify the parts of prisms and cylinders
• find the volumes and surface area of standard
three dimensional objects: cylinders, prisms, pyramids, cones, and spheres
COURSE OUTLINE:
A. The Language of Geometry
1) The coordinate plane
2) Points, lines, planes
3) Problem-solving strategies
4) The measure of a segment
5) Segment relationships
6) Rays and angles
7) Classifying angles
8) Pairs of angles
B. Reasoning and Introduction to Proofs
1) If-then statements, converses
2) Properties from algebra
3) Two column proofs with segments
4) Two column proofs with angles
C. Parallels
1) Parallels and transversals
2) Using parallel lines
3) Proving lines parallel
4) Slopes and lines
5) Parallels and distance
D. Congruent triangles
1) Classifying triangles
2) Angle measure in triangles
3) Congruent triangles
4) Tests for congruent triangles
5) Another test for congruent triangles
6) Isosceles triangles
E. Applying Congruent Triangles
1) Special segments in triangles
2) Right triangles
3) Inequalities for sides and angles of a triangle
4) The triangle inequality
5) Inequalities involving two triangles
F. Quadrilaterals
1) Parallelograms
2) Tests for parallelograms
3) Rectangles
4) Squares and rhombi
5) Trapezoids
G. Similarity
1) Properties of proportions
2) Applications of proportions
3) Similar polygons
4) Similar triangles
5) Proportional parts
6) Parts of similar triangles
H. Right Triangles and Trigonometry
1) The geometric mean
2) The Pythagorean theorem
3) Special right triangles
4) Trigonometry
5) Applications: using trigonometry
I. Circles
1) Parts of circles
2) Angles and arcs
3) Arcs and chords
4) Inscribed angles
5) Tangents
6) More angle measure
7) Special segments in a circle
J. Polygons and Areas
1) Angles of Polygons
2) Area of Parallelograms
3) Area of triangles, rhombi, and trapezoids
4) Area and circumference of a circle
K. Surface Area and Volume
1) Exploring surface area
3) Surface area of prisms and cylinders
4) Surface area of pyramids and cones
5) Volume of prisms and cylinders
6) Volume of pyramids and cones
7) Surface area and volume of spheres
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