correlated to the

Washington D.C. Public Schools Learning Standards Geometry

McDougal Littell Geometry ©2007

correlated to the

Washington DC Public Schools

Learning Standards Geometry

G.G.1 Know correct geometric notation, including the notation for line segment (AB) and angle

(<ABC).

PE/TE: Lesson 1.1: Identify Points, Lines and Planes, 3 Lesson 1.4: Measure and Classify Angles, 24

G.G.2 Recognize special types of polygons (e.g., isosceles triangles, parallelograms, and rhombuses).

PE/TE: Lesson 4.1: Apply Triangle Sum Properties, 217, 221 (#9) Activity 8.2: Investigate Parallelograms, 514 Lesson 8.4: Properties of Rhombuses, Rectangles and Squares, 533

G.G.3 Apply properties of sides, diagonals, and angles in special polygons; identify their parts and

special segments (e.g., altitudes, midsegments); determine interior angles for regular polygons.

PE/TE: Lesson 4.1: Apply Triangle Sum Properties, 218 Lesson 5.1: Mid-segment Theorem and Coordinate Proof, 295, 298 (#3-5) Lesson 5.4: Use Medians and Altitudes, 320, 323 (#23, 24) Lesson 8.2: Use Properties of Parallelograms, 515-520 Lesson 8.3: Show that a Quadrilateral is a Parallelogram, 523-524, 526 (#8-10), 527 (#19-21) Lesson 8.4: Properties of Rhombuses, Rectangles and Squares, 533, 535, 537 (#3-8, 19-24), 538 (#32-37)

G.G.4 Draw and label sets of points such as line segments, rays and circles.

PE/TE: Lesson 1.1: Identify Points, Lines and Planes, 6 (#25-26) Activity 10.1: Explore Tangent Segments, 650 Activity 10.4: Explore Inscribed Angles, 671

G.G.5 Detect symmetries of geometric figures.

PE/TE: Lesson 1.6: Classify Poliygons, 47 Lesson 9.6: Identify Symmetry, 619-623, 624 (#35) Chapter Review: 639 (#17-19)

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McDougal Littell Geometry ©2007 correlated to the Washington DC Public Schools Learning Standards: Geometry G.G.6 Apply the triangle inequality and other inequalities associated with triangles (e.g., the longest

side is opposite the greatest angle) to prove theorems and to solve problems.

PE/TE: Lesson 5.5: Use Inequalities in a Triangle, 328-334 Lesson 5.6: Inequalities in Two Triangles and Indirect Proof, 335-340 Chapter Review: 347 (#19-26)

G.G.7 Use properties and theorems about congruent and similar figures and about perpendicular and

parallel lines to solve problems.

PE/TE: Lesson 3.3: Prove Lines are Parallel, 161, 162 (#3-5), 164 (#6-8), 165-168, 169 (#39-44) Lesson 3.6: Prove Theorems About Perpendicular Lines, 191 (#1), 192 (#3-4), 194, 195 (#15-21) Lesson 4.2: Apply Congruence and Triangles, 226 (#1-3), 227 (#4-5), 228-230 Activity 6.3: Similar Polygons, 371 Lesson 6.3: Use Similar Polygons, 372-378, 379 (#35-39) Lesson 6.4: Prove Triangles Similar by AA, 381-386, 387 (#37) Lesson 6.5: Prove Triangles Similar by SSS and SAS, 388-394, 395 (#37-38) Lesson 7.3: Use Similar Right Triangles, 450 (#1-2), 453, 454 (#13-18)

G.G.8 Write simple proofs of theorems in geometric situations, such as theorems about triangles,

congruent and similar figures, and perpendicular and parallel lines (e.g., the longest side is opposite the greatest angle, two lines parallel to a third are parallel to each other; perpendicular bisectors of line segments are the set of all points equidistant from the two end points).

PE/TE: Lesson 3.3: Prove Lines are Parallel, 164 (#6), 166 (#19-21, 25), 167 (#31), 168 (#38)

Lesson 3.4: Find and Use Slopes of Lines, 177 (#38) Lesson 3.6: Prove Theorems About Perpendicular Lines, 191 (#2), 194 (#8-10) Lesson 4.2: Apply Congruence and Triangles, 231 (#31) Lesson 5.2: Use Perpendicular Bisectors, 307 (#23), 308 (#26-27), 309 (#32) Lesson 6.4: Prove Triangles Similar by AA, 386 (#35-36) Lesson 6.5: Prove Triangles Similar by SSS and SAS, 395 (#37)

G.G.9 Distinguish between postulates and theorems. Use inductive and deductive reasoning, as well as

proof by contradiction. Given a conditional statement, write its inverse, converse, and contrapositive.

PE/TE: Lesson 1.2: Use Segments and Congruence, 9

Lesson 2.2: Analyze Conditional Statements, 80, 83 (#7-10), 84 (#26-28, 34), 85 (#36) Lesson 2.6: Prove Statements About Segments and Angles, 113 Chapter Review: 135 (#6) Lesson 5.6: Inequalities in Two Triangles and Indirect Proof, 337 (#4), 339 (#11-13), 340 (#23), 341 (#27)

G.G.10 Apply formulas for a rectangular coordinate system to justify theorems.

PE/TE: Lesson 5.1: Midsegment Theorem and Coordinate Proof, 297, 300 (#36-37), 301 (#42)

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McDougal Littell Geometry ©2007 correlated to the Washington DC Public Schools Learning Standards: Geometry G.G.11 Draw congruent and similar figures using a compass, straightedge, or protractor.

Justify the constructions by logical argument.

PE/TE: Activity 4.3: Investigate Congruent Figures, 233 Lesson 4.3: Prove Triangles Congruent by SSS, 235

Activity 4.4: Investigate Triangles and Congruence, 247 Lesson 4.6: Use Congruent Triangles, 258, 261 (#32) Lesson 6.4: Prove Triangles Similar by AA, 381 Lesson 6.7: Perform Similarity Transformations, 409, 412 (#3-8)

G.G.12 Apply congruence and similarity correspondences (e.g., ∆ABC ≅ ∆XYZ) and properties of the figures to find missing parts of geometric figures, and provide logical justification.

PE/TE: Lesson 1.4: Measure and Classify Angles, 27 (#6), 30 (#28)

Lesson 2.6: Prove Statements About Segments and Angles, 117 (#17-18) Lesson 4.2: Apply Congruence and Triangles, 228 (#5-10), 229 (#19-21) Lesson 4.6: Use Congruent Triangles, 259 (#13) Lesson 6.4: Prove Triangles Similar by AA, 383 (#4), 386 (#32)

G.G.13 Apply properties of angles, parallel lines, arcs, radii, chords, tangents, and secants to solve

problems.

PE/TE: Lesson 1.4: Measure and Classify Angles, 31 (#51-55), 32 (#52-62) Lesson 1.5: Describe Angle Pair Relationships, 40 (#53) Activity 2.7: Angles and Intersecting Lines, 122-123 Lesson 2.7: Prove Angle Pair Relationships, 128 Lesson 3.2: Use Parallel Lines and Transversals, 154-159 Lesson 5.3: Use Angle Bisectors of Triangles, 311-312, 313 (#12-14) Lesson 10.2: Find Arc Measures, 661 (#3-10), 662 Lesson 10.3: Apply Properties of Chords, 667-669 Lesson 10.5: Apply Other Angle Relationships in Circles, 680-684, 685 (#22) Lesson 10.6: Find Segment Lengths in Circles, 689-694, 695 (#34-39) Lesson 10.7: Write and Graph Equations of Circles, 705 (#52-54)

G.G.14 Solve simple triangle problems using the triangle angle sum property and/or the Pythagorean

theorem; study and understand more than one proof of this theorem.

PE/TE: Lesson 4.1: Apply Triangle Sum Properties, 218-223 Activity 7.1: Pythagorean Theorem, 432 Lesson 7.1: Apply the Pythagorean Theorem, 433-434, 436, 437 (#6-10, 14-17), 438, 439 (#35) Lesson 7.3: Use Similar Right Triangles, 455 (#32)

G.G.15 Use the properties of special triangles (e.g., isosceles, equilateral, 30º-60º-90º, 45º-45º-90º) to

solve problems.

PE/TE: Lesson 4.7: Use Isosceles and Equilateral Triangles, 266-270 Lesson 7.4: Special Right Triangles, 461-463, 464 (#34-35)

3

McDougal Littell Geometry ©2007 correlated to the Washington DC Public Schools Learning Standards: Geometry G.G.16 Define the sine, cosine and tangent of an acute angle. Apply to the solution of problems.

PE/TE: Lesson 7.5: Apply the Tangent Ratio, 466-467, 469 (#3-5) Lesson 7.6: Apply the Sine and Cosine Ratios, 473, 477 (#3-5, 7-9)

G.G.17 Demonstrate an understanding of the relationship between various representations of a line.

Determine a line's slope and x- and y-intercepts from its graph or from a linear equation that represents the line. Find a linear equation describing a line from a graph or a geometric description of the line (e.g., by using the point-slope or slope y-intercept formulas). Explain the significance of a positive, negative, zero, or undefined slope.

PE/TE: Lesson 3.4: Find and Use Slopes of Lines, 171-177

Activity 3.4: Investigate Slopes, 179 Lesson 3.5: Write and Graph Equations of Lines, 180-184, 185 (#23-25, 49-52), 186 (#60-61) Chapter Review: 205 (#25-26)

Chapter Test: 206 (#13-21, 25) Skills Review Handbook: 879

G.G.18 Using rectangular coordinates, calculate midpoints of segments, slopes of lines and segments,

and distances between two points and apply the results to the solutions of problems.

PE/TE: Lesson 1.3: Use Midpoint and Distance Formulas, 17-18, 19 (#17-22), 20 (#31-33) Lesson 1.7: Find Perimeter, Circumference and Area, 50, 51 (#5), 53 (#16-19) Lesson 3.4: Find and Use Slopes of Lines, 175 (#13-15), 176 (#23-25) Chapter Review: 204 (#23-24) Lesson 8.2: Use Properties of Parallelograms 517, 518 (#16)

G.G.19 Find linear equations that represent lines either perpendicular or parallel to a given line and

through a point (e.g., by using the point-slope form of the equation).

PE/TE: Lesson 3.5: Write and Graph Equations of Lines, 180-181, 185 (#23-35) G.G.20 Draw the results and interpret transformations on figures in the coordinate plane such as

translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solution of problems.

PE/TE: Lesson 4.8: Perform Congruence Transformations, 273-275, 276 (#3-5, 9-12),

277 (#20-23), 279 (#4-8) Lesson 6.7: Perform Similarity Transformations, 409-411, 413 (#19-20), 415 (#4-5) Activity 9.3: Reflections in the Plane, 588 Lesson 9.3: Perform Reflections, 589-590, 593 (#3-12)

G.G.21 Demonstrate the ability to visualize solid objects and recognize their projections, cross sections,

and graph points in 3-D.

PE/TE: Extension 8.5: Draw Three-Dimensional Figures, 550-551 Activity 12.1: Investigate Solids, 792-793 Lesson 12.1: Explore Solids, 797, 799 (#25-27), 800 (#40-41) Activity 12.2: Investigate Surface Area, 802 Lesson 12.2: Surface Area of Prisms and Cylinders, 803, 805

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McDougal Littell Geometry ©2007 correlated to the Washington DC Public Schools Learning Standards: Geometry G.G.22 Find and use measures of perimeter, circumference, and area of common geometric figures such

as parallelograms, trapezoids, circles, and triangles.

PE/TE: Lesson 1.7: Find Perimeter, Circumference and Area, 52 (#4-9), 53 (#11-19), 55 (#44, 46), 56 (#4-6) Lesson 10.7: Write and Graph Equations of Circles, 705 (#46-51) Lesson 11.1: Areas of Triangles and Parallelogram, 720-725 Activity 11.2: Areas of Trapezoids and Kites, 729 Lesson 11.2: Areas of Trapezoids, Rhombuses and Kites, 730, 733 (#3-6), 734 (#31)

G.G.23 Find and use measures of lateral areas, surface areas, and volumes of prisms, pyramids, spheres,

cylinders, and cones, and relate these measures to each other using formulas.

PE/TE: Activity 12.2: Investigate Surface Area, 802 Lesson 12.2: Surface Area of Prisms and Cylinders, 803-809 Lesson 12.3: Surface Area of Pyramids and Cones, 810-816, 817 (#2-7) Lesson 12.4: Volume of Prisms and Cylinders, 819-825 Activity 12.5: Investigate the Volume of a Pyramid, 828

Lesson 12.5: Volume of Pyramids and Cones, 829-835, 836 (#1-7) Lesson 12.6: Surface Area and Volume of Spheres, 838-845

G.G.24 Relate changes in the measurement (including units) of one attribute of an object to changes in

other attributes.

PE/TE: Activity 1.7: Investigate Perimeter and Area, 48 Lesson 6.3: Use Similar Polygons, 374 Lesson 11.3: Perimeter and Area of Similar Figures, 737-743 Activity 12.5: Minimize Surface Area, 837 Activity 12.7: Investigate Similar Solids, 846 Lesson 12.7: Explore Similar Solids, 848-849

G.G.25 Describe the effects of approximate error in measurement and rounding on measurements and on

computed values from measurements.

PE/TE: Extension 11.1: Determine Precision and Accuracy, 727-728 G.G.26 Use dimensional analysis for unit conversion and to confirm that expressions and equations

make sense.

PE/TE: Lesson 1.7: Find Perimeter, Circumference and Area, 51, 53 (#20-26) Lesson 11.1: Areas of Triangles and Parallelogram, 722 Lesson 11.3: Perimeter and Area of Similar Figures, 739 Skills Review Handbook, 886

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DC 316/2007

2007 CC2