MATH 139 - Plane Geometry Fall 2008

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Oct 10, 2013 (4 years and 1 day ago)

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SLO: Math 139


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MATH 139

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Plane Geometry







Fall 2008


Student Learning Outcomes:


Upon successful completion of the course, the student will be able to:


1.
Determine the validity of arguments using tautologies and Euler Circles.


2.
Construct geometric figures

using a straightedge and compass.


3.
Write direct and indirect proofs of theorems and corollaries.


4.
Solve problems involving geometric figures using definitions, postulates, and theorems.


Student Performance Objectives:


1. Understand and explain

the vocabulary of plane geometry and deductive logic including
hypothesis, conclusion, converse, inverse, and contrapositive.


2. Write proofs of theorems and corollaries related to geometric figures, using deductive
reasoning.


3. Solve problems which re
quire properties of parallel and perpendicular lines, trapezoids and
parallelograms, circles, tangents, secants, and

chords.


4. Set up proportions and solve them to find unknown parts of similar figures.


5. Use the Law of Pythagoras and its converse to s
olve problems.


6. Use right triangle trigonometry to find unknown parts of right triangles.


7. Solve problems concerning regular polygons and circular regions.


8. Use fundamental locus theorems to find the locus of a point satisfying given conditions.


9. Solve simple problems involving coordinate geometry.


10. Construct geometric figures using straightedge and compass.


11. Prove inequality theorems using indirect reasoning and use inequalities to solve problems
using geometric figures.

Course Content
Outline:


Study of deductive proofs.

Identify the hypothesis and conclusion of a theorem; write the converse, inverse, or
contrapositive of a theorem.

SLO: Math 139


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Indirect reasoning in proofs
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identify faulty reasoning; e.g. "circular" "by analogy".

Inductive reasoni
ng
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discover geometric properties by measurement.

Geometric terms
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e.g. point, line, plane, angle, triangle, altitude, perimeter, square, diagonal,
circle, diameter; adjacent, corresponding, interior.

Notation and symbols of geometry (||,|, ~, ~, )<, etc
.)

Measurement: angles, line segments; conversion from one system of measurement to another.

Basic properties of all triangles (e.g. sum of angles is 180 ); theorems of congruence.

Special properties of isosceles, equilateral, right triangles (including th
e Pythagorean theorem).

Properties of parallel and perpendicular lines.

Properties of quadrilaterals: parallelogram, rectangle, rhombus, trapezoid.

Properties of general polygons (n
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gons); special properties of regular polygons.

Properties of circles; cent
ral and inscribed angles, arc, chord, tangent.

Similarity theorems, including proportions of similar polygons.

Area formulas and theorems.

Locus; be able to determine loci, use locus theorems.

Introduce analytical geometry
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solving problems involving rect
angular coordinate system in the
plane, distance formula, slope, equations of lines and circles.

Properties of geometric inequalities (e.g. in a triangle, the longest side is opposite the largest
angle).

Constructions (with compass and straightedge).