and Curriculum Framework Publisher: McGraw-Hill School Education Text: Geometry Copyright date 2018 G.1 The student will use deductive reasoning to construct and judge the validity of a logical argument consisting of a set of premises and a conclusion. This will include a) identifying the converse, inverse, and contrapositive of a conditional statement; TE: 119-130, 151#12-#13, 205 #14-#19 b) translating a short verbal argument into symbolic form; and TE: 119-130, 131-130, 141-150, 151 #17-#18, 152-158, 159-168, 206 #20-#27, 207 #28-#34 c) determining the validity of a logical argument. TE: 119-130, 131-130, 141-150, 151 #12-#13, 206 #20-#22 Geometry Lab 140 Geometry 1 of 15 Virginia Department of Education 2017
and Curriculum Framework G.2 The student will use the relationships between angles formed by two lines intersected by a transversal to a) prove two or more lines are parallel; and TE: 186-193, 210 #61-#65, 214 #4 b) solve problems, including practical problems, involving angles formed when parallel lines are intersected by a transversal. TE: 169-176, 186-193, 208 #35-#46, 210 #61-#65, 211 #13-#15, 214 #4 Geometry Software Lab 168 Geometry 2 of 15 Virginia Department of Education 2017
and Curriculum Framework G.3 The student will solve problems involving symmetry and transformation. This will include a) investigating and using formulas for determining distance, midpoint, and slope; TE: 14-25, 26-35, 45 #7-#10, 98 #18-#24, 178-184, 209 #47-#59, 211 #16-#17 Graphing Technology Lab 177 b) applying slope to verify and determine whether lines are parallel or perpendicular; TE: 178-184, 209 #47-#50, 211 #18 Geometry Lab 531-532 c) investigating symmetry and determining whether a figure is symmetric with respect to a line or a point; and d) determining whether a figure has been translated, reflected, rotated, or dilated, using coordinate methods. TE: 259-265, 272 #28-#32, 273 #16, 276 #2, 277 #11 TE: 221-229, 232-238, 240-247, 249-258 Geometry Lab 219-220,230-231, 239, 248 Geometry 3 of 15 Virginia Department of Education 2017
and Curriculum Framework G.4 The student will construct and justify the constructions of a) a line segment congruent to a given line segment; TE: 16, 22 #50, 25 #66 Key Concept 16 b) the perpendicular bisector of a line segment; TE: Geometry Lab 353 c) a perpendicular to a given line from a point not on the line; TE: Geometry Lab 55 d) a perpendicular to a given line at a given point on the line; TE: 201 Geometry Lab 55 Geometry 4 of 15 Virginia Department of Education 2017
and Curriculum Framework G.4 The student will construct and justify the constructions of e) the bisector of a given angle; TE: 40 Geometry Lab 309 f) an angle congruent to a given angle; TE: 39 g) a line parallel to a given line through a point not on the line; and TE: 186 h) an equilateral triangle, a square, and a regular hexagon inscribed in a circle. TE: Geometry Lab 686 Geometry 5 of 15 Virginia Department of Education 2017
and Curriculum Framework G.5 The student, given information concerning the lengths of sides and/or measures of angles in triangles, will solve problems, including practical problems. This will include a) ordering the sides by length, given angle measures; TE: 374-380, 413 #17-#19 b) ordering the angles by degree measure, given side lengths; TE: 374-380, 381 #54, 413 #17-#19 c) determining whether a triangle exists; and TE: 394-400, 414 #26-#30, 418 #6 Graphing Technology Lab 393 d) determining the range in which the length of the third side must lie. TE: 394-400, 414 #26-#30, 415 #24-#25 Geometry 6 of 15 Virginia Department of Education 2017
and Curriculum Framework G.6 The student, given information in the form of a figure or statement, will prove two triangles are congruent. TE: 291-299, 300-308, 310 #20, 311-318, 319-324, 342 #16-#18, 343 #19-#24, 344 #25-#26 Geometry 7 of 15 Virginia Department of Education 2017
and Curriculum Framework G.7 The student, given information in the form of a figure or statement, will prove two triangles are similar. TE: 502-510, 511-520, 521-530, 533 #13, 555 #15-#19, 557 #9, 559, 561 #11 Geometry 8 of 15 Virginia Department of Education 2017
and Curriculum Framework G.8 The student will solve problems, including practical problems, involving right triangles. This will include applying a) the Pythagorean Theorem and its converse; TE: 575-583, 607 #11, 631 #14-#19, 635 #6, 637, 638 #1 Geometry Lab 574 b) properties of special right triangles; and TE: 586-594, 607 #12-#13, 632 #20-#22, 635 #19 c) trigonometric ratios. TE: 596-605, 607 #17-#21, 608-615, 632 #23-#31, 633 #32-#33, 635 #10-#13 Graphing Technology Lab 595, 606 Geometry 9 of 15 Virginia Department of Education 2017
and Curriculum Framework G.9 The student will verify and use properties of quadrilaterals to solve problems, including practical problems. TE: 433-441, 443-451, 452 #23, 453-459, 460-468, 469-478, 480 #22 Geometry Software Lab 442 Geometry 10 of 15 Virginia Department of Education 2017
and Curriculum Framework G.10 The student will solve problems, including practical problems, involving angles of convex polygons. This will include determining the a) sum of the interior and/or exterior angles; TE: 423-431, 452 #1-#4, 480 #11-#12, 483 #1-#2 Spreadsheet Lab 432 b) measure of an interior and/or exterior angle; and TE: 423-431, 452 #11-#12 Spreadsheet Lab 432 c) number of sides of a regular polygon. TE: 423-431, 452 #7-#10, 480 #14-#15, 483 #7-#10 Spreadsheet Lab 432 Geometry 11 of 15 Virginia Department of Education 2017
and Curriculum Framework G.11 The student will solve problems, including practical problems, by applying properties of circles. This will include determining a) angle measures formed by intersecting chords, secants, and/or tangents; TE: 652-660, 661-668, 669-676, 677 #14, 678-685, 687-695, 712 #17-#18, 713 #24-#25 b) lengths of segments formed by intersecting chords, secants, and/or tangents; TE: 661-668, 669-676, 677#11, 678-685, 687-695, 713 #22, 714 #28, 717 #7 c) arc length; and TE: 652-660, 661-668, 669-676, 677 #7, 712 #19, 713 #21, 714 #30, 717 #5 d) area of a sector. TE: 743-749, 784 #21-#24, 787 #14, 791 #12 Geometry 12 of 15 Virginia Department of Education 2017
and Curriculum Framework G.12 The student will solve problems involving equations of circles. TE: 696-702, 715, 717 #14-#15, 720 #2 Geometry 13 of 15 Virginia Department of Education 2017
and Curriculum Framework G.13 The student will use surface area and volume of threedimensional objects to solve practical problems. TE: 76-83, 103 #23-#24, 770-781, 786, 787 #19, 802-809, 810-816, 818-825 Geometry 14 of 15 Virginia Department of Education 2017
and Curriculum Framework G.14 The student will apply the concepts of similarity to twoor three-dimensional geometric figures. This will include a) comparing ratios between lengths, perimeters, areas, and volumes of similar figures; TE: 502-510, 519 #33, 763-769, 785 #30-#32, 790 #1, 834-840, 850 #31-#33, 851 #20 b) determining how changes in one or more dimensions of a figure affect area and/or volume of the figure; TE: 62 #29, 82 #35, 763-769, 785 #30-#32, 790 #1, 834-840, 850 #31-#33, 851 #20 c) determining how changes in area and/or volume of a figure affect one or more dimensions of the figure; and TE: 502-510, 519 #33, 763-769, 785 #30-#32, 790 #1, 834-840, 850 #31-#33, 851 #20 d) solving problems, including practical problems, about similar geometric figures. TE: 502-510, 519 #33, 763-769, 785 #30-#32, 790 #1, 834-840, 850 #31-#33, 851 #20 Geometry 15 of 15 Virginia Department of Education 2017