Categorieën: Alle - probability - similarity

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Carnegie Geometry Two

The content covers a range of geometric and mathematical concepts, primarily focusing on the properties and classifications of various shapes and forms. Key topics include the study of quadrilaterals and their specific types such as parallelograms, rhombi, kites, trapezoids, squares, and rectangles, alongside their interior and exterior angles.

Carnegie Geometry Two

Carnegie Geometry

13. Circles on coordinate plane

Equation of a Parabola
Circles and points on the coordinate plane
Determining points on a circle
Equation of a circle
Circles on coordinate plane problems

14. Independence and Conditional Probability

Theoretical and Experimental Probability
Calculating compound probability
Compound probability with "or"
Compound Probability with "and"
Compound sample space
Modeling probability

15. Probability of Compound Events

Expected values
Independent Trials
Permutations and Combinations
Conditional probability
Two way Tables

1. Tools of Geometry

Points of concurrency
Parallel lines, perpendicular lines and polygons
Parallel and perpendicular lines in coordinate plane
Angle and angle bisectors
Midpoint and bisectors
Translating and constructing line segments
Points, lines, planes, rays, segments

2. Logic and Proof

Parallel line converse theorems
Angle Postulates and theorems
Forms of Proof
Special angles and postulates
Foundations of proof

3. Perimeter and Area of geometric figures on the coordinate plane

Area of circle
circumference of circle
Area and perimeter of composite figures on coordinate plane
Area and perimeter of trapezoidal on coordinate plane
area and perimeter of parallelograms on coordinate plane
Area and Perimeter of triangles on coordinate plane
Using transformations to determine perimeter and area

4. Volume and surface area

Diagonals in three dimensions
Cross Sections
Applying Volume formulas
Volume of sphere
Volume of Cones and Pyramids
Translating Two-dimensional figures
Rotating two-dimensional figures

5. Right Triangle Geometry

30-60-90 triangle
45-45-90 triangle
triangle inequality theorem
Triangle sum theorem
Classifying triangles

12. More Circles

Circle Word Problems
Sectors and segments
Arc Length
Inscribed triangles and quadrilaterals

11. Circles

Tangents and circles
Chords
Measuring angles inside and outside of circles
Central angles, Inscribed Angles, Intercepted Arcs
Circle vocabulary

10. Quadrilaterals

Identifying Quadrilaterals in the coordinate plane
Quadrilateral family properties
Exterior angles of a polygon
Interior angles of a polygon
Kites and Trapezoids
Parallelograms and Rhombi
Squares ans Rectangles

9. Right Triangle Trigonometry

Applying Law of sines and law of cosines
Law of sines Law of cosines
Angles of elevation and depression
Complement angle relationship
Cosines ratio
Sine ratio
Tangent ratio

8. Congruence

Direct proof vs. Indirect proof
Isosceles Triangle Theorem
CPCTC
Right triangle congruence

7. Congruence

Applying congruent triangles
AAS congruence
ASA congruence
SAS congruence
SSS congruence
Congruent triangles
Translating, rotating, reflecting geometric figures

6. Similarity

Cavalieri's principle
Applying Similar Triangles
Proving Pythagorean theorem
Geometric Mean
Theorems about proportionality
Similar triangle theorems
Dialating triangles