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Geometry Course Description


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Unit 1: Basic Theories, Defns, and Symbols of Geometry

    *Basic terms of geometry such as

collinear, coplanar, segment, ray, angle, figure, intersection, and space

    * symbols for geometric figures

    * Properties of Line Segments

    * angle types and properties such as acute, right, obtuse, straight, reflex, complementary, supplementary, linear, pair, congruent, and angle bisectors

    * Constructions

    * Measuring with geometric tools and algebraic methods

 

Unit 2: Linear Relationships (2 weeks)

·         Definitions of types of lines and planes such as parallel, perpendicular, oblique, skew

·         Parallel lines and Transversals

·         Slope Concepts

Unit 1: Basic Theories, Defns, and Symbols of Geometry

  1. Students will define and identify the basic terms of geometry and correctly use symbols to denote each concept.
  2. Students will apply the properties of segments to geometric and real-world problems.
  3. Students will define, recognize, and apply angle types, pairs and properties.
  4. Students will integrate basic constructions into the discovery of geometric principles.
  5. Students will use appropriate tools and methods (algebraic integrated and distance formula) to measure both segments and angles.

 

Unit 2: Linear Relationships (2 weeks)

  1. Students will apply properties of different types of lines and planes.
  2. Students will discover relationships among angles formed by transversals.
  3. Students will understand and apply the concept of slope in mathematical and real-world situations including parallel and perpendicular lines.

·         Equations of Lines (including parallel and perpendicular)

·         Linear Correlation

 

Unit 3: Congruent Triangles

·         Triangle Classification

·         Angles of Triangles

·         Triangle Congruence

·         Properties of Isosceles, Equilateral, and Right Triangles

Unit 4: Properties of Triangles

·         Special segments of triangles

·         Points of concurrency

  1. Students will find equations of parallel and perpendicular lines.
  2. Students will investigate real-world data using lines of best fit.

 

Unit 3: Congruent Triangles
  1. Students will classify triangles according to sides and angles.
  2. Students will apply triangle angle relationships in real-world problems
  3. Students will apply and understand triangle congruence shortcuts with and without a coordinate system.
  4. Students will discover and utilize properties of isosceles, equilateral, and right triangles with and without a coordinate system. 

 

Unit 4: Properties of Triangles

  1. Students will define and apply the properties of medians, altitudes, bisectors, and midsegments in triangles.
  2. Students will construct points of concurrency such as circumcenter, incenter, orthocenter, and centroid and understand real-world connections.

·         Triangle Inequalities

·         Triangles on the Coordinate System

Unit 5: Quadrilaterals and Polygons

·         Classification of Polygons

·         Angle Relationships of Polygons

·         Quadrilateral Classification and Properties

 

Unit 6: Patterns and Transformations

·         Transformations such as Translations, Rotations, Reflections, and Dilations

·         Transformations in the Coordinate Plane

·         Reflectional and Rotational Symmetry

·         Patterns and Inductive Reasoning (incorporated in other units)

  1. Students will discover, understand, and apply triangle inequality theories such as the Hinge Theorem.
  2. Students will apply all of the above with and without the coordinate system.

 

Unit 5: Quadrilaterals and Polygons

  1. Students will classify polygons by number of sides and shape.
  2. Students will discover and apply relationships between interior and exterior angles of polygons.
  3. Students will classify quadrilaterals according to properties.
  4. Students will apply properties of parallelograms, rectangles, rhombi, squares, trapezoids, and kites to real-world problems with and without a coordinate system.

Unit 6: Patterns and Transformations

  1. Students will apply transformations to figures and compare corresponding parts
  2. Students will discover and apply coordinate transformations.
  3. Students will examine shapes for different types of symmetry.
  4. Students will investigate patterns through inductive reasoning.  (incorporated in other units)
Unit 6: Patterns and Transformations

·         Transformations such as Translations, Rotations, Reflections, and Dilations

·         Transformations in the Coordinate Plane

·         Reflectional and Rotational Symmetry

·         Patterns and Inductive Reasoning (incorporated in other units)

 
 
Unit 7: Similarity and Similar Triangles

·         Ratio and Proportion

·         Similar Polygons

·         Similar Triangles

·         Indirect Measurement

 

Unit 8:  Circles

·         Parts of Circles

·         Angle and Segment Properties of Circles

 

Unit 6: Patterns and Transformations

  1. Students will apply transformations to figures and compare corresponding parts
  2. Students will discover and apply coordinate transformations.
  3. Students will examine shapes for different types of symmetry.
  4. Students will investigate patterns through inductive reasoning.  (incorporated in other units)
 
 
Unit 7: Similarity and Similar Triangles
  1. Students will apply the concepts of ratio and proportion to real-world problems.
  2. Students will understand the concept of similarity and apply the concept to a real-world setting.
  3. Students will prove triangles similar and solve problems using similar triangles.
  4. Students will solve real-world problems using indirect measurement techniques.
 
Unit 8:  Circles
  1. Students will define and symbolize all parts of circles
  2. Students will apply properties of segments and angles of circles.

 Unit 8:  Circles

·         Parts of Circles

·         Angle and Segment Properties of Circles

 Unit 8:  Circles

1 Students will define and symbolize all parts of circles

2.Students will apply properties of segments and angles of circles.

Geometry - State Standards Taught

The geometry skills and concepts developed in this discipline are useful to all

students. Aside from learning these skills and concepts, students will develop their

ability to construct formal, logical arguments and proofs in geometric settings and

problems.

1.0 Students demonstrate understanding by identifying and giving examples of

undefined terms, axioms, theorems, and inductive and deductive reasoning.

2.0 Students write geometric proofs, including proofs by contradiction.

3.0 Students construct and judge the validity of a logical argument and give

counterexamples to disprove a statement.

4.0 Students prove basic theorems involving congruence and similarity.

5.0 Students prove that triangles are congruent or similar, and they are able to use

the concept of corresponding parts of congruent triangles.

6.0 Students know and are able to use the triangle inequality theorem.

7.0 Students prove and use theorems involving the properties of parallel lines cut by

a transversal, the properties of quadrilaterals, and the properties of circles.

8.0 Students know, derive, and solve problems involving the perimeter, circumference,

area, volume, lateral area, and surface area of common geometric figures.

9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders,

cones, and spheres; and students commit to memory the formulas for prisms,

pyramids, and cylinders.

10.0 Students compute areas of polygons, including rectangles, scalene triangles,

equilateral triangles, rhombi, parallelograms, and trapezoids.

11.0 Students determine how changes in dimensions affect the perimeter, area, and

volume of common geometric figures and solids.

12.0 Students find and use measures of sides and of interior and exterior angles of

triangles and polygons to classify figures and solve problems.

13.0 Students prove relationships between angles in polygons by using properties of

complementary, supplementary, vertical, and exterior angles.

14.0 Students prove the Pythagorean theorem.

15.0 Students use the Pythagorean theorem to determine distance and find missing

lengths of sides of right triangles.

16.0 Students perform basic constructions with a straightedge and compass, such as

angle bisectors, perpendicular bisectors, and the line parallel to a given line

through a point off the line.

17.0 Students prove theorems by using coordinate geometry, including the midpoint

of a line segment, the distance formula, and various forms of equations of lines

and circles.

18.0 Students know the definitions of the basic trigonometric functions defined by

the angles of a right triangle. They also know and are able to use elementary

relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 +

(cos(x)) 2 = 1.

19.0 Students use trigonometric functions to solve for an unknown length of a side of

a right triangle, given an angle and a length of a side.

20.0 Students know and are able to use angle and side relationships in problems with

special right triangles, such as 30, 60, and 90?triangles and 45, 45, and 90°

triangles.

21.0 Students prove and solve problems regarding relationships among chords,

secants, tangents, inscribed angles, and inscribed and circumscribed polygons

of circles.

22.0 Students know the effect of rigid motions on figures in the coordinate plane and

space, including rotations, translations, and reflections.

 

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