PREREQUISITE – Successful completion of Algebra I

 

DESCRIPTION – Geometry will emphasize the use of deductive reasoning to prove the common facts of plane and solid geometry.  Emphasis will also be placed on reading and oral communications, recognition of symbols, definitions of mathematical terms, and the ability to relate the readings of diagrams, charts, and figures.

 

CONTENT

1.  Understand the basic terms and symbols of geometry.
1. Know the undefined terms.
2. Be able to identify basic geometric shapes, symbols, and drawings (ray, line segment, angle).

 

2. Know how to measure segments and angles.
1. Use a ruler and protractor.
2. Use the Distance Formula to find the length of a segment.
3. Use addition postulates.
4. Find the coordinates of the midpoint or endpoint of a segment.

 

3.  Be able to apply deductive and inductive reasoning.
1. Know the different types of conditional statements.
2. Know and apply the definitions, postulates, and theorems of Geometry and the properties of Algebra.
3. Be able to write a deductive reasoning argument in paragraph form and/or two-column form.
4. Be able to use inductive reasoning to make a conjecture.
5. Be able to find and write a counterexample.

 

4. Understand the relationships formed by perpendicular lines, parallel lines, and parallel planes.
1. Understand and apply the basic definitions and properties of perpendicular lines, parallel lines and parallel planes.
2. Apply the properties of parallel lines to prove lines parallel.

 

5. Understand the properties of triangles.
1. Be able to prove triangles congruent.
2. Use congruent triangles to solve problems.
3. Know and apply theorems based on congruent triangles.
4. Know and apply midsegments, and altitudes of triangles.

 

6. Understand properties of quadrilaterals and other polygons.
1. Know and apply properties and theorems of polygons.
2. Know and apply properties and theorems of quadrilaterals.
3. Know and apply the properties of parallelograms, rectangles, squares, and rhombuses.
4. Know and apply the properties of trapezoids and kites.

 

7. Understand inequalities in geometry.
1. Know basic inequalities in geometry.
2. Apply the method of indirect proof.
3. Apply inequalities to triangles.

 

8. Understand the concepts of similarity.
1. Know and apply the properties of proportions.
2. Apply proportions to similar polygons.
3. Use similar triangles to solve problems.

 

9. Understand the properties of right triangles.
1. Know and apply the Pythagorean theorem.
2. Know and apply the properties of special right triangles.
3. Know and apply right triangle trigonometry.

 

10. Understand the properties of circles.
1. Know the basic terms.
2. Know and apply the relationships between circles and angles.
3. Know and apply the relationships between circles and lines.

 

11. Understand area, perimeter and volume.
1. Be able to apply the basic formulas of polygons and circles.
2. Be able to find the areas and volumes of solids.
3. Be able to apply the basic formulas to life problems.

 

12. Be able to use geometric instruments and make drawings. *
1. Be able to identify basic construction instruments.
2. Be able to perform basic constructions.

 

13. Be able to apply geometry to the coordinate system. *
1. Know and apply the concept of slope.
2. Be able to solve, graph and derive linear equations.
3. Apply coordinate geometry to proofs.

 

14. Understand transformations. *
1. Be able to perform basic mappings.
2. Know and apply composition and symmetry.

 

*THESE ITEMS ARE COVERED IF TIME ALLOWS.