Carnegie Geometry Two

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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