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Student Edition Lesson(s) |
| 1.0 |
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Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning. |
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1-1, 2-1, 2-4, 2-5, 2-6, 3-1 |
| 2.0 |
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Students write geometric proofs, including proofs by contradiction. |
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2-5, 2-6, 2-7, 2-8, 3-2, 3-5, 3-6, 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7, 5-1, 5-2, 5-3, 5-4, 5-5, 6-3, 6-4, 6-5, 7-1, 7-2, 7-6, 7-7, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, 9-5, 10-2, 10-3, 10-4, 10-5, 10-6, 10-7 |
| 3.0 |
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Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement. |
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2-1, 2-2, 2-3, 2-4, 6-2, 6-4, 8-3, 8-4 |
| 4.0 |
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Students prove basic theorems involving congruence and similarity. |
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2-7, 2-8, 4-3, 4-4, 4-5, 4-6, 6-3, 6-5, 7-1, 8-2, 8-5, 8-6 |
| 5.0 |
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Students 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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4-3, 4-4, 4-5, 4-6, 6-2, 6-3, 6-5, 6-6 |
| 6.0 |
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Students know and are able to use the triangle inequality theorem. |
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5-4, 5-5 |
| 7.0 |
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Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. |
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3-2, 3-5, 6-4, 8-2, 8-3, 8-4, 8-5, 8-6, 8-7, 10-2, 10-3, 10-4, 10-5, 10-6, 10-7 |
| 8.0 |
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Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. |
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1-6, 6-5, 10-1, 11-1, 11-2, 11-3, 11-4, 11-5, 12-2, 12-3, 12-4, 12-5, 12-6, 12-7, 13-1, 13-2, 13-3, 13-4 |
| 9.0 |
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Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to memory the formulas for prisms, pyramids, and cylinders. |
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12-2, 12-3, 12-4, 12-5, 12-6, 12-7, 13-1, 13-2, 13-3 |
| 10.0 |
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Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids. |
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11-1, 11-2, 11-3, 11-4 |
| 11.0 |
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Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and solids. |
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1-6, 6-2, 9-5, 11-1, 11-2, 13-4 |
| 12.0 |
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Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and solve problems. |
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4-1, 4-2, 4-3, 5-1, 5-2, 5-4, 6-3, 6-4, 6-5, 7-1, 8-1, 8-2, 8-3, 8-4, 8-5, 8-6 |
| 13.0 |
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Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical, and exterior angles. |
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4-2, 5-2, 5-3, 5-4, 8-2, 8-3 |
| 14.0 |
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Students prove the Pythagorean theorem. |
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7-2 |
| 15.0 |
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Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles. |
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1-3, 7-2, 7-3, 9-6 |
| 16.0 |
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Students perform basic constructions 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. |
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1-2, 1-3, 1-4, 3-5, 4-4, 4-5, 6-4, 8-4, 8-5, 8-6, 10-3, 10-5, 10-4 |
| 17.0 |
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Students 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. |
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3-6, 4-7, 6-4, 8-7, 10-8 |
| 18.0 |
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Students know the definitions of the basic trigonometric functions defined by the angles of a right triangle. They also know and are able to use elementary relationships between them. For example, tan(x) = sin(x)/cos(x), (sin(x))2 + (cos(x))2 = 1. |
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7-4 |
| 19.0 |
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Students use trigonometric functions to solve for an unknown length of a side of a right triangle, given an angle and a length of a side. |
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7-4, 7-5, 9-6, 13-2 |
| 20.0 |
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Students know and are able to use angle and side relationships in problems with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles. |
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7-3, 13-2 |
| 21.0 |
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Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles. |
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10-3, 10-4, 10-5, 10-4, 10-6, 10-7 |
| 22.0 |
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Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations, and reflections. |
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9-1, 9-2, 9-3, 9-6, 9-7, 13-5 |
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Extra Examples—
—Standards Practice