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correlated to

UtahCore Curriculumfor MathematicsGeometry

Utah Core Curriculum for Mathematics

Geometry

correlated to

McDougal Littell Geometry ©2007

McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Chapter 1 Essentials of Geometry (pp. 1 - 69) Lesson 1.1 (pp. 2 – 8) Identify Points, Lines, and Planes

Lesson 1.2 (pp. 9 – 14) Use Segments and Congruence

Lesson 1.3 (pp. 15 – 23) Use Midpoint and Distance Formulas

2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices.

Lesson 1.4 (pp. 24 – 34) Measure and Classify Angles

2.2.f Model and solve geometric situations using algebraic properties. 3.3.a Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

Lesson 1.5 (pp. 35 – 41) Describe Angle Pair Relationships

3.1.d Identify angle pairs as adjacent, complementary, supplementary, a linear pair, or vertical angles.

Lesson 1.6 (pp. 42 – 48) Classify Polygons

Lesson 1.7 (pp. 49 – 58) Find Perimeter, Circumference, and Area

2.2.f Model and solve geometric situations using algebraic properties.

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Utah Core Curriculum for Mathematics: Geometry correlated to McDougal Littell Geometry ©2007

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Chapter 2 Reasoning and Proof (pp. 70 - 143)

Lesson 2.1 (pp. 72 – 78 ) Use Inductive Reasoning

3.1.c Prove a statement false by using a counterexample.

Lesson 2.2 (pp. 79 – 86) Analyze Conditional Statements

3.1.b Write conditional statements, converses, and inverses and determine the truth value of the statements. 3.1.c Prove a statement false by using a counterexample.

Lesson 2.3 (pp. 87 – 95) Apply Deductive Reasoning

3.1.c Prove a statement false by using a counterexample.

Lesson 2.4 (pp. 96 – 104) Use Postulates and Diagrams

3.1.b Write conditional statements, converses, and inverses and determine the truth value of the statements 3.1.c Prove a statement false by using a counterexample.

Lesson 2.5 (pp. 105 – 111) Reason Using Properies from Algebra

3.1.c Prove a statement false by using a counterexample.

Lesson 2.6 (pp. 112 – 123) Prove Statements about Segments and Angles

Lesson 2.7 (pp. 124 – 132) Prove Angle Pair Relationships

3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities.

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Chapter 3 Parallel and Perpendicular Lines (pp. 144 - 213) Lesson 3.1 (pp. 147 – 153) Identify Pairs of Lines and Angles

3.1.e Differentiate between parallel, perpendicular, skew, and intersecting lines. 3.1.f Classify angle pairs formed by two lines and a transversal, e.g., corresponding, alternate interior, and supplementary angles. 3.3.a Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

Lesson 3.2 (pp. 154 – 160) Use Parallel Lines and Transversals

2.2.f Model and solve geometric situations using algebraic properties. 3.1.b Write conditional statements, converses, and inverses and determine the truth value of the statements. 3.1.f Classify angle pairs formed by two lines and a transversal, e.g., corresponding, alternate interior, and supplementary angles. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 3.3 (pp. 161 – 170) Prove Lines are Parallel

2.2.f Model and solve geometric situations using algebraic properties. 3.1.e Differentiate between parallel, perpendicular, skew, and intersecting lines. 3.1.f Classify angle pairs formed by two lines and a transversal, e.g., corresponding, alternate interior, and supplementary angles. 3.1.g Prove lines parallel or perpendicular using slope or angle relationships. 3.3.a Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

Lesson 3.4 (pp. 171 – 179) Find and Use Slopes of Lines

Utah Core Curriculum for Mathematics: Geometry correlated to McDougal Littell Geometry ©2007

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Lesson 3.5 (pp. 180 – 189) Write and Graph Equations of Lines

2.2.e Write an equation of a line perpendicular or parallel to a line through a given point. 2.2.f Model and solve geometric situations using algebraic properties.

Lesson 3.6 (pp. 190 – 199) Prove Theorems about Perpendicular Lines

2.2.e Write an equation of a line perpendicular or parallel to a line through a given point. 3.1.g Prove lines parallel or perpendicular using slope or angle relationships. 3.3.a Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Chapter 4 Congruent Triangles (pp. 217 - 294) Lesson 4.1 (pp. 217 – 224) Apply Triangle Sum Properties

2.2.f Model and solve geometric situations using algebraic properties. 3.1.l Classify and use the properties of acute, right, scalene, obtuse, isosceles, equilateral, or equiangular triangles. 3.2.c Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula.

Lesson 4.2 (pp. 225 – 233) Apply Congruence and Triangles

2.2.f Model and solve geometric situations using algebraic properties. 3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.1.b. Write conditional statements, converses, and inverses and determine the truth value of the statements.

Lesson 4.3 (pp. 234 – 239) Prove Triangles Congruent by SSS

2.2.e Write an equation of a line perpendicular or parallel to a line through a given point. 3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.1.h Prove congruency and similarity of geometric figures. 3.1.l Classify and use the properties of acute, right, scalene, obtuse, isosceles, equilateral, or equiangular triangles.

Lesson 4.4 (pp. 240 – 248) Prove Triangles Congruent by SAS and HL

2.2.e Write an equation of a line perpendicular or parallel to a line through a given point. 3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.1.h Prove congruency and similarity of geometric figures.

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Lesson 4.5 (pp. 249 – 255) Prove Triangles Congruent by ASA and AAS

2.2.e Write an equation of a line perpendicular or parallel to a line through a given point. 3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.1.h Prove congruency and similarity of geometric figures.

Lesson 4.6 (pp. 256 – 263) Use Congruent Triangles

2.2.f Model and solve geometric situations using algebraic properties. 3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities.

Lesson 4.7 (pp. 264 – 271) Use Isosceles and Equilateral Triangles

2.2.f Model and solve geometric situations using algebraic properties. 3.1.l Classify and use the properties of acute, right, scalene, obtuse, isosceles, equilateral, or equiangular triangles. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 4.8 (pp. 272 – 280) Perform Congruence Transformations

3.1.h Prove congruency and similarity of geometric figures. 3.1.l Classify and use the properties of acute, right, scalene, obtuse, isosceles, equilateral, or equiangular triangles. 3.2.c Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula. 3.2.d Perform and analyze transformations (translations, rotations, reflections, and dilations) using coordinate geometry.

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Chapter 5 Relationships within Triangles (pp. 295 - 353) Lesson 5.1 (pp. 295 – 302) Mid-segment Theorem and Coordinate Proof

3.1.h Prove congruency and similarity of geometric figures. 3.2.c Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 5.2 (pp. 303 – 309 ) Use Perpendicular Bisectors

2.2.f Model and solve geometric situations using algebraic properties. 3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities 3.1.i Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle. 3.3.a Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives.

Lesson 5.3 (pp. 310 – 318) Use Angle Bisectors of Triangles

2.2.f Model and solve geometric situations using algebraic properties. 3.1.i Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle. 3.3.a Construct/copy angles and segments, bisect angles and segments, and create perpendicular lines and parallel lines using a compass and straight edge, technology, or other manipulatives. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Utah Core Curriculum for Mathematics: Geometry correlated to McDougal Littell Geometry ©2007

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Lesson 5.4 (pp. 319 – 325) Use Medians and Altitudes

2.2.f Model and solve geometric situations using algebraic properties. 3.1.i Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle.

Lesson 5.5 (pp. 328 – 334) Use Inequalities in a Triangle

3.1.b Write conditional statements, converses, and inverses and determine the truth value of the statements. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 5.6 (pp. 335 – 342) Inequalities in Two Triangles and Indirect Proof

2.2.f Model and solve geometric situations using algebraic properties. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Chapter 6 Similarity (pp. 356 - 432) Lesson 6.1 (pp. 356 – 363) Ratios, Proportions, and the Geometric Mean

2.2.e Write an equation of a line perpendicular or parallel to a line through a given point. 2.2.f Model and solve geometric situations using algebraic properties.

Lesson 6.2 (pp. 364 – 371) Use Proportions to Solve Geometry Problems

Lesson 6.3 (pp. 372 – 380) Use Similar Polygons

2.2.f Model and solve geometric situations using algebraic properties. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 6.4 (pp. 381 – 387) Prove Triangles Similar by AA

3.1.f Classify angle pairs formed by two lines and a transversal, e.g., corresponding, alternate interior, and supplementary angles. 3.1.h Prove congruency and similarity of geometric figures. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 6.5 (pp. 388 – 396) Prove Triangles Similar by SSS and SAS

2.2.f Model and solve geometric situations using algebraic properties. 3.1.h Prove congruency and similarity of geometric figures. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

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McDougal Littell Geometry ©2007

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Lesson 6.6 (pp. 397 – 408) Use Proportionality Theorems

2.2.f Model and solve geometric situations using algebraic properties. 3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 6.7 (pp. 409 – 416) Perform Similarity Transformations

3.2.d Perform and analyze transformations (translations, rotations, reflections, and dilations) using coordinate geometry. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

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McDougal Littell Geometry ©2007

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Chapter 7 Right Triangles and Trigonometry (pp. 433 - 506) Lesson 7.1 (pp. 433 – 440) Apply the Pythagorean Theorem

3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 7.2 (pp. 441 – 448) Use the Converse of the Pythagorean Theorem

3.1.i Identify medians, altitudes, and angle bisectors of a triangle, and the perpendicular bisectors of the sides of a triangle. 3.1.l Classify and use the properties of acute, right, scalene, obtuse, isosceles, equilateral, or equiangular triangles. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 7.3 (pp. 449 – 456) Use Similar Right Triangles

Lesson 7.4 (pp. 457 – 465) Special Right Triangles

2.1.c Solve problems using the properties of special right triangles, e.g., 30°, 60°, 90° or 45°, 45°, 90°. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

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Lesson 7.5 (pp. 466 – 472) Apply the Tangent Ratio

2.1.a Identify trigonometric relationships (sine, cosine, and tangent) using right triangles, expressing the relationships as fractions or decimals. 2.1.c Solve problems using the properties of special right triangles, e.g., 30°, 60°, 90° or 45°, 45°, 90°. 2.2.b Find the trigonometric ratio given the angle measure in degrees using a calculator. 2.2.c Find the missing measures of right triangles. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 7.6 (pp. 473 – 482) Apply the Sine and Cosine Ratios

2.1.a Identify trigonometric relationships (sine, cosine, and tangent) using right triangles, expressing the relationships as fractions or decimals. 2.1.c Solve problems using the properties of special right triangles, e.g., 30°, 60°, 90° or 45°, 45°, 90°. 2.2.b Find the trigonometric ratio given the angle measure in degrees using a calculator. 2.2.c Find the missing measures of right triangles. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

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Lesson 7.7 (pp. 483 – 492) Solve Right Triangles

2.1.c Solve problems using the properties of special right triangles, e.g., 30°, 60°, 90° or 45°, 45°, 90°. 2.2.a Find the angle measure in degrees given the trigonometric ratio using a calculator. 2.2.b Find the trigonometric ratio given the angle measure in degrees using a calculator. 2.2.c Find the missing measures of right triangles. 2.2.d Find missing parts of triangles using the Law of Sines or Law of Cosines. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Utah Core Curriculum for Mathematics: Geometry correlated to McDougal Littell Geometry ©2007

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Chapter 8 Quadrilaterals (pp. 507 – 571) Lesson 8.1 (pp. 507 – 514) Find Angle Measures in Polygons

2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices. 2.2.a Find the angle measure in degrees given the trigonometric ratio using a calculator.

Lesson 8.2 (pp. 515 – 521) Use Properties of Parallelograms

2.2.b Find the trigonometric ratio given the angle measure in degrees using a calculator.

Lesson 8.3 (pp. 522 – 531) Show that a Quadrilateral is a Parallelogram

3.2.c Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula.

Lesson 8.4 (pp. 533 – 541) Properties of Rhombuses, Rectangles, and Squares

Lesson 8.5 (pp. 542 – 551) Use Properties of Trapezoids and Kites

3.2.c Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula.

Lesson 8.6 (pp. 552 – 558) Identify Special Quadrilaterals

3.1.j Classify a quadrilateral as a parallelogram, trapezoid, rectangle, square, rhombus, kite, or none of the above. 3.2.c Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula.

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Chapter 9 Properties of Transformations (pp. 572 – 650) Lesson 9.1 (pp. 572 – 579) Translate Figures and Use Vectors

3.1.j Classify a quadrilateral as a parallelogram, trapezoid, rectangle, square, rhombus, kite, or none of the above. 3.2.c Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula. 3.2.d Perform and analyze transformations (translations, rotations, reflections, and dilations) using coordinate geometry.

Lesson 9.2 (pp. 580 – 588) Use Properties of Matrices

Lesson 9.3 (pp. 589 – 597) Perform Reflections

3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.2.d Perform and analyze transformations (translations, rotations, reflections, and dilations) using coordinate geometry.

Lesson 9.4 (pp. 598 – 607) Perform Rotations

3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities.

Lesson 9.5 (pp. 608 – 618) Apply Compositions of Transformations

3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities.

Lesson 9.6 (pp. 619 – 625) Identify Symmetry

Lesson 9.7 (pp. 626 – 634) Identify and Perform Dilations

3.2.d Perform and analyze transformations (translations, rotations, reflections, and dilations) using coordinate geometry.

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McDougal Littell Geometry ©2007

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Chapter 10 Properties of Circles (pp. 651 – 719) Lesson 10.1 (pp. 651 – 658) Use Properties of Tangents

3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.1.k Identify radii, diameters, chords, secants, arcs, sectors, central angles, inscribed angles, and tangents for circles.

Lesson 10.2 (pp. 659 – 663) Find Arc Measures

3.1.k Identify radii, diameters, chords, secants, arcs, sectors, central angles, inscribed angles, and tangents for circles. 3.3.c Identify the relationships between the measures of intercepted arcs and inscribed or central angles.

Lesson 10.3 (pp. 664 – 671) Apply Properties of Chords

2.2.f Model and solve geometric situations using algebraic properties. 3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.1.j Classify a quadrilateral as a parallelogram, trapezoid, rectangle, square, rhombus, kite, or none of the above. 3.2.c Verify the classifications of geometric figures using coordinate geometry to find lengths and slopes, e.g., verify or prove the diagonals of a rectangle are congruent using the distance formula. 3.3.c Identify the relationships between the measures of intercepted arcs and inscribed or central angles.

Lesson 10.4 (pp. 672 – 679) Use Inscribed Angles and Polygons

3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.1.k Identify radii, diameters, chords, secants, arcs, sectors, central angles, inscribed angles, and tangents for circles. 3.3.c Identify the relationships between the measures of intercepted arcs and inscribed or central angles.

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Lesson 10.5 (pp. 680 – 688) Apply Other Angle Relationships in Circles

3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 10.6 (pp. 689 – 695) Find Segment Lengths in Circles

3.1.a Use accepted geometric notations, e.g., congruencies, transformations, similarities. 3.3.c Identify the relationships between the measures of intercepted arcs and inscribed or central angles. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 10.7 (pp. 699 – 706) Write and Graph Equations of Circles

3.2.a Graph a circle given the equation in the form (x - h)2 + (y - k)2 = r2. 3.2.b Write the equation of a circle given its graph with the center of the circle at the origin.

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Chapter 11 Measuring Length and Area (pp. 720 – 793) Lesson 11.1 (pp. 720 – 729) Areas of Triangles and Parallelograms

2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices. 3.3.d Solve real-world problems using geometric properties, trigonometric ratios and properties of congruent and similar figures, e.g., “How much paint is needed to paint a room?” or “How can we ensure square corners in a building during construction?”

Lesson 11.2 (pp. 730 – 736) Areas of Trapezoids, Rhombuses, and Kites

2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices. 2.1.d Identify the effect on area or volume when changing linear dimensions.

Lesson 11.3 (pp. 737 – 745) Perimeter and Area of Similar Figures

2.1.d Identify the effect on area or volume when changing linear dimensions.

Lesson 11.4 (pp. 746 – 754) Circumference and Arc Length

3.3.b Define π as the ratio of the circumference to the diameter of a circle. 3.3.c Identify the relationships between the measures of intercepted arcs and inscribed or central angles. 4.1.b Find the length of an arc and the area of a sector.

Lesson 11.5 (pp. 755 – 761) 2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices. 3.3.c Identify the relationships between the measures of intercepted arcs and inscribed or central angles. 4.1.b Find the length of an arc and the area of a sector.

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Lesson 11.6 (pp. 762 – 770) Areas of Regular Polygons

2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices. 4.1.a Find the area of a regular polygon. 5.1.b Calculate geometric probability.

Lesson 11.7 (pp. 771 – 778) Use Geometric Probability

4.1.a Find the area of a regular polygon. 4.1.d Estimate the area of an irregular region. 5.1.a Identify geometric probabilities by performing simulations involving length or area. 5.1.b Calculate geometric probability.

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Chapter 12 Surface Area and Volume of Solids (pp. 794 – 865) Lesson 12.1 (pp. 792 – 802) Explore Solids

2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices. 3.1.m Classify polyhedrons and other three-dimensional figures according to their properties. 3.3.e Sketch cross-sections of geometric solids. 4.1.a Find the area of a regular polygon.

Lesson 12.2 (pp. 803 – 809) Surface Area of Prisms and Cylinders

2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices. 2.1.d Identify the effect on area or volume when changing linear dimensions. 4.1.a Find the area of a regular polygon. 4.1.c Find the surface area and volume for prisms, cylinders, pyramids, cones, and spheres given the formula.

Lesson 12.3 (pp. 810 – 818) Surface Area of Pyramids and Cones

4.1.c Find the surface area and volume for prisms, cylinders, pyramids, cones, and spheres given the formula.

Lesson 12.4 (pp. 819 – 828) Volume of Prisms and Cylinders

2.1.b Analyze geometric patterns to develop formulas and communicate how the formulas were derived, e.g., angle measure and number of sides of a polygon, interior and exterior angles, diagonals, and vertices. 4.1.c Find the surface area and volume for prisms, cylinders, pyramids, cones, and spheres given the formula.

Lesson 12.5 (pp. 829 – 837) Volume of Pyramids and Cones

2.1.d Identify the effect on area or volume when changing linear dimensions. 3.1.k Identify radii, diameters, chords, secants, arcs, sectors, central angles, inscribed angles, and tangents for circles. 4.1.c Find the surface area and volume for prisms, cylinders, pyramids, cones, and spheres given the formula.

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McDougal Littell Geometry ©2007

Utah Core Curriculum for Mathematics

Lesson 12.6 (pp. 838 – 846) Surface Area and Volume of Spheres

4.1.c Find the surface area and volume for prisms, cylinders, pyramids, cones, and spheres given the formula. 5.1.b Calculate geometric probability.

Lesson 12.7 (pp. 847 – 855) Explore Similar Solids

4.1.c Find the surface area and volume for prisms, cylinders, pyramids, cones, and spheres given the formula.

UT 19911/2006

2007 CC2