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Course Description
This course covers essential introductory components of geometry. It implements appropriate grade level strands, unifying ideas, and standards from the Mathematics Content Standards for California Public Schools, (California Department of Education, 2001), and Principals and Standards for School Mathematics Grades 9-12. (National Council of Teachers of Mathematics, 2000). The use of computers and graphing calculators are encouraged. Problems are designed to engage higher order thinking processes in a collaborative environment. These learning opportunities are provided equitably for all students through the use of mathematical ideas, tools, and techniques.
Credits: 5
Released: 2005
Course Content
Introduction to Basic Geometry, Definitions and Constructions Unit 1
- Demonstrate understanding of mathematical concepts through research and writing exercises
- Use compass and straight edge to construct segments and segment bisectors
- Demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning
- Perform basic construction 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
- Construct angles, angle bisector, perpendicular bisector, perpendicular lines, and parallel lines
- Use construction to derive angle theorems
- Measure angles and solve diagrams using properties of angles
- Prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles
- Prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles
- Use construction to derive triangle theorems
- Solve problems using properties of triangles
- Know and use the triangle inequality theorem
- Sketch diagrams to demonstrate understanding of theorems of parallelograms
- Solve problems using properties and theorems of polygons
- Prove basic theorems involving congruence and similarity
- Find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems
Congruency Unit 2
- Triangle congruence theorems (SSS, SAS, AAS, ASA)
- Prove basic theorems involving congruence and similarity
- Prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles
- Know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures
- Find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems
- Prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles
- Perform basic construction 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
- Apply triangle congruency theorems to polygons
- Applications of congruency
- Prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles
Similarity Unit 3
- Express ratios and proportions in simplest form
- Solve proportions for unknown variables
- Demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning
- Find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems
- Investigate the relationship between proportion and scale factor
- Demonstrate understanding of scale factor through construction and writing
- Prove basic theorems involving congruence and similarity
- Find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems
- Investigate properties of similar polygons
- Apply ratio, proportion, and scale factor to similarity problems using triangles
- Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles
- Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles
- Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles
Pythagorean Theorem and Special Right Triangles Unit 4
- Coordinate plane
- Demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning
- Use Pythagorean Theorem
- Know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures
- Compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids
- Find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems
- Prove the Pythagorean theorem
- Use the Pythagorean theorem to determine distance and finding missing lengths of sides of right triangles
- Find distance between any two points of a line
- Find slope of a line
- Use slope to identify whether two lines are parallel or perpendicular
- Perform basic construction 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
- 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
- Use Pythagorean Theorem and ratio with special right triangles and circles
- Prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles
- Know and are able to use angles and side relationships in problems with special right triangles, such as 30o, 60o, and 90o triangles and 45o, 45o, and 90o triangles
- Prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles
Circles Unit 5
- Demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning
- Know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures
- Compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids
- Find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems
- Perform basic construction 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
- Prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles
- Introduce concept of tangency
- Solve problems using tangents, secants, and chords
- Apply properties of circles to real-world applications
- Prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles
- Prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles
- Use the Pythagorean theorem to determine distance and finding missing lengths of sides of right triangles
- Know and use angles and side relationships in problems with special right triangles, such as 30o, 60o, and 90o triangles and 45o, 45o, and 90o triangles
- Find the circumference and area of circles
- Find the sector area of circles
- Use deductive reasoning to prove theorems related to the properties of circles, tangents, arcs, and chords
- Use inductive reasoning to discover properties related to circles
- Write geometric proofs, including proofs by contradiction
- Prove basic theorems involving congruence and similarity
- Prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of congruent triangles
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