Download GEOMETRY

GEOMETRY
CONTENT OFFERED IN CARNEGIE LEARNING® MATH CURRICULA SOLUTIONS
Textbook
Cognitive Tutor® Software
Skills Covered
Print Chapter
Software Unit
The student will:
1. Tools of Geometry
2. Parallel and
Perpendicular Lines
3. Area and Perimeter
4. Triangles
5. Similarity
6. Congruence
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1.
2.
3.
4.
Lines, Rays, Segments, and Angles
Angles and Angle Pairs
Angle Properties
Proofs with Segments and Angles
5.
6.
7.
8.
Lines Cut by Transversals
Proofs with Parallel Lines
Triangle Classification
Polygon Classification
9. Perimeter and Area of Squares and Rectangles
10. Perimeter and Area of Parallelograms
11. Perimeter and Area of Triangles
12. Perimeter and Area of Trapezoids
13. Circumference and Area of Circles
14. Area Composition
15. Perimeter and Area of Regular Polygons
16.
17.
18.
19.
Triangle Properties, Part 1
Proofs with Triangles
Pythagorean Theorem
Special Right Triangles
20. Ratios and Proportions
21. Similar Triangles
•Name points, lines, rays, line segments, and planes.
•Describe the intersection of lines and planes.
•Add and subtract line segments.
•Name and classify angles and classify angle pairs.
•Calculate measures of angles.
•Construct duplicate line segments and angles, angle bisectors, perpendiculars, perpendicular bisectors, and midpoints.
•Define and use inductive and deductive reasoning.
•Identify the hypothesis and conclusion of a conditional statement.
•Use truth tables.
•Prove angle theorems using two-column, flow chart, paragraph, and construction proofs.
• Classify angles formed by two lines cut by a transversal.
•Prove theorems involving parallel lines cut by a transversal.
•Prove converse theorems involving parallel lines cut by a transversal.
•Classify polygons by the number of sides, concave or convex, and regular or irregular.
•Define parts of a polygon including diagonals, consecutive sides and angles, and opposite sides and angles.
•Classify triangles and quadrilaterals.
• Calculate perimeters of polygons.
•Calculate areas of polygons.
•Calculate unknown measures of polygons.
•Calculate circumferences of circles.
•Calculate areas of circles.
•Calculate areas of composite figures.
•Determine the effect of altering dimensions on perimeter and area.
•Construct squares, rectangles, isosceles triangles, and isosceles trapezoids.
• Prove theorems involving triangles including Triangle Sum Theorem, Exterior Angle Theorem, Exterior Angle Inequality Theorem, and Triangle Inequality Theorem.
•Use the Pythagorean Theorem and the Converse of the
Pythagorean Theorem.
•Calculate side length of 30º -60º -90º triangles and 45º -45º -90º triangles.
•Explore the relationships between the side lengths of a triangle and the
measures of its interior angles.
• Write and solve proportions.
•Calculate angle measures and side lengths of similar polygons.
•Compare ratios of perimeters and areas of similar polygons.
•Make conjuectures and prove that two triangles are similar using triangle similarity postulates.
•Construct similar triangles.
•Prove the Angle Bisector / Proportional Sides Theorem.
•Use geometric means.
• Construct congruent triangles.
•Prove triangles congruent using SSS, SAS, ASA, AAS, HL, LL, HA, and LA 22. Triangle Properties, Part 2
Congruence Theorems.
23. Proofs with Congruent Triangles
•Prove angles and segments are congruent using congruent parts of 24. Proofs of Theorems using Congruent congruent triangles.
Triangles
•Prove theorems involving isosceles triangles using congruent triangles and corresponding parts.
•Prove the Hinge Theorem and Converse using indirect proof.
CONTENT OFFERED IN CARNEGIE LEARNING® MATH CURRICULA SOLUTIONS
Textbook
Cognitive Tutor® Software
Skills Covered
Print Chapter
Software Unit
The student will:
7.Right Triangle Trigonometry
8.Quadrilaterals
9.Geometry in the Coordinate Plane
25. Right Triangles and Trigonometric Functions
26.
27.
28.
Properties of Quadrilaterals and Parallelograms
Properties of Trapezoids and Rectangles
Properties of Rhombi
29. Finding Equations of a Line
30. Distance and Midpoint
10.Simple
Transformations
31. Geometric Transformations
11.Circles
32.
33.
34.
Central and Inscribed Angles
in Circles
Circle Chords
Interior and Exterior Angles in Circles
12.Volume and
Surface Area
35.
36.
37.
38.
39.
40.
41.
Volume and Surface Area of
Right Prisms
Volume and Surface Area of Cylinders
Volume of Pyramids
Volume of Cones
Volume and Surface Area of Spheres
Quadratic Equation Solving
Backwards Volume and Surface Area
13. More in Three Dimensions
14. Vectors
•Calculate the tangent, cotangent, sine, cosecant, cosine, and secant of an angle as a ratio of side lengths.
•Use trigonometric functions to solve for angle measures and side lengths.
•Calculate angles of elevation and depression.
• Conjecture and prove the properties of squares, rectangles, parallelograms, rhombi, kites, and trapezoids.
•Construct quadrilaterals.
•Calculate angle measures and side lengths of quadrilaterals using properties of quadrilaterals.
•Prove biconditional statements.
•Calculate sums of interior and exterior angles of polygons.
•Categorize quadrilaterals based upon their properties.
•Derive and use the Distance Formula and Midpoint Formula.
•Explore parallel and perpendicular lines in the coordinate plane.
•Calculate the distance between a line and a point not on the line.
•Identify and use properties of midsegments of triangles.
•Prove the Triangle Midsegment Theorem and the Trapezoid
Midsegment Theorem.
•Construct points of concurrency of triangles.
•Calculate points of concurrency of triangles algebraically.
•Classify triangles and quadrilaterals in the coordinate plane.
• Reflect, rotate, translate, and dilate points and figures in the
coordinate plane.
•Describe transformations using coordinate notation.
•Determine rotational, vertical, and horizontal symmetry of figures.
•Explore fractals and tessellations.
• Identify and draw parts of a circle.
•Calculate measures of arcs, central angles, inscribed angles, interior angles, and exterior angles of circles.
•Prove theorems involving circles.
•Determine properties of inscribed and circumscribed circles.
•Calculate arc lengths.
•Calculate areas of sectors and segments of circles.
•Explore properties of circles in the coordinate plane.
•Identify the vertices, edges, and faces of polyhedra.
•Create nets for polyhedron.
•Calculate the volume of prisms, cylinders, pyramids, cones, and spheres.
•Determine the effect of altering dimensions on volume and surface area.
•Calculate the surface area of prisms, cylinders, pyramids, cones,
and spheres.
•Calculate the surface area of composite solids.
•Determine cross sections of planes and solids.
•Use Euler’s Formula.
•Create traversable and non-traversable networks.
•Draw vertex-edge graphs and directed graphs.
•Model and solve problems using vertex-edge graphs and directed graphs.
•Draw the top, side, and front views of a solid using isometric drawings.
•Draw isometric drawings using top, side, and front views.
•Use the Pythagorean Theorem in three dimensions.
•Define vectors using vector notation and column vector notation.
•Calculate the magnitude of vectors.
•Draw vectors.
•Add and subtract vectors using the Triangle Rule of Vector Addition and the Parallelogram Rule of Vector Addition.
•Calculate the measure of a directional angle.
•Multiply a vector by a scalar.
•Determine the components of a vector using magnitude and
directional angle.
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