Download Geometry - McDougal Littell

Utah
Core Curriculum
for Mathematics
Geometry
correlated to
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.
1
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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.
2
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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
3
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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.
4
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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.
5
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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.
6
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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?”
7
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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?”
8
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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?”
9
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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?”
10
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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?”
11
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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?”
12
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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?”
13
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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.
14
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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.
15
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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.
16
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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.
17
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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.
18
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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.
19
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
McDougal Littell
Geometry ©2007
Utah
Core Curriculum for Mathematics
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 threedimensional 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.
20
Utah Core Curriculum for Mathematics: Geometry correlated to
McDougal Littell Geometry ©2007
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.
21
UT 199
11/2006
2007
CC2