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Geom_3eTE.03EM.X_189-193 3/24/06 11:13 AM Page 189 Chapter 3 Chapter Review 3 Chapter Review Vocabulary Review Resources equilateral polygon (p. 160) exterior angle of a polygon (p. 149) flow proof (p. 135) isosceles triangle (p. 148) obtuse triangle (p. 148) point-slope form (p. 168) polygon (p. 157) regular polygon (p. 160) remote interior angles (p. 149) acute triangle (p. 148) alternate exterior angles (p. 129) alternate interior angles (p. 127) concave polygon (p. 158) convex polygon (p. 158) corresponding angles (p. 127) equiangular triangle (p. 148) equiangular polygon (p. 160) equilateral triangle (p. 148) right triangle (p. 148) same-side exterior angles (p. 129) same-side interior angles (p. 127) scalene triangle (p. 148) slope-intercept form (p. 166) standard form of a linear equation (p. 167) transversal (p. 127) two-column proof (p. 129) Student Edition Extra Skills, Word Problems, Proof Practice, Ch. 3, p. 720 English/Spanish Glossary, p. 779 Postulates and Theorems, p. 770 Table of Symbols, p. 763 Vocabulary and Study Skills worksheet 3F Spanish Vocabulary and Study Skills worksheet 3F Interactive Textbook Audio Glossary Online Vocabulary Quiz Choose the correct vocabulary term to complete each sentence. 1. In a triangle, an angle is right, obtuse, or 9. acute 2. A(n) 9 angle has a measure between 90 and 180. obtuse 3. When two coplanar lines are cut by a transversal, two angles that are in similar positions on the same side of the transversal are called 9. corresponding angles 4. The measure of a(n) 9 angle of a triangle is equal to the sum of the measures of its two remote interior angles. exterior 5. A polygon is 9 if no diagonal contains points outside the polygon. convex 6. A(n) 9 polygon has all angles congruent. equiangular 7. A(n) 9 polygon is both equiangular and equilateral. regular PHSchool.com For: Vocabulary quiz Web Code: auj-0351 8. The linear equation y - 3 = 4(x + 5) is written in 9 form. point-slope 9. From the 9 form of a linear equation, you can easily read the value of the slope and the value of the y-intercept. slope-intercept 10. When two coplanar lines are cut by a transversal, the angles between the two lines and on opposite sides of the transversal are called 9. alternate interior angles Spanish Vocabulary/Study Skills Skills and Concepts Vocabulary/Study Skills Name Class 3D: Vocabulary To identify angles formed by two lines and a transversal To prove and use properties of parallel lines t A transversal is a line that intersects two coplanar lines at two distinct points. &1 and &4 are corresponding angles. &3 and &4 are alternate interior angles. &2 and &4 are same-side interior angles. Study Skill: You will encounter many new terms as you read a mathematics textbook. Read aloud or recite the new terms as you read them. This will help you remember and recall rules, definitions and formulas for future use. It is important to learn the definitions of new terms as soon as they are introduced and continue to increase your vocabulary. ᐉ 1 2 L3 Date For use with Chapter Review Unscramble the UPPERCASE letters to form a math word or phrase that completes each sentence. Copy the letters in the numbered cells to the cells with the same number at the bottom of the page. 3 1. COOPDUNM EUNIISAQELTI are joined by and or or. 4 k 6 16 13 2. An TEITINYD is an equation that is true for every value. 19 20 3 3. The NRGEA of a set of data is the difference between the greatest and least data values. 5 If two parallel lines are cut by a transversal, then 4. A data value that is much higher or lower than the other data in a set is an LEUTORI. 9 5. An XENNPTEO shows repeated multiplication. • corresponding angles are congruent. 28 15 14 6. A coordinate plane is divided by its axes into four TANQAUSRD. • alternate interior angles are congruent. 2 23 25 7. You IMPIYSLF an equation when you replace it with its simplest name or form. 32 1 © Pearson Education, Inc. All rights reserved. 3-1 Objectives ELL 22 8. A EVBALRAI is a symbol, usually a letter, which represents one or more numbers. • same-side interior angles are supplementary. 12 18 9. The numerical factor when a term has a variable is a CINCEFFITOE. 11. Suppose / and k in the diagram above are parallel. If m&1 = 59, what are the measures of &2, &3, and &4? ml2 121, ml3 59, ml4 59 26 21 31 4 8 17 11 11. The multiplicative inverse of a number is always its RLREIPACCO. 30 1 Chapter 3 Chapter Review 10 27 24 29 10. LOHWE SURBEMN are the nonnegative integers. 189 2 3 7 4 5 6 7 8 9 10 11 12 13 14 4 15 16 17 18 19 20 21 22 23 4 24 25 26 27 28 29 30 31 32 12 Reading and Math Literacy Masters Algebra 1 189 Geom_3eTE.03EM.X_189-193 3/24/06 11:13 AM Page 190 13. ml1 75; same side int. ' are suppl. ml2 105; alt. int. ' are O or two ' that form a straight l are suppl. 14. ml1 55; same side int. ' are suppl. ml2 90; alt. int. ' are O. Find m&1 and then m&2. Justify each answer. 13–14. See margin. 12. ml1 120; corr. ' are O. ml2 120; vert. ' are O or alt. ext. ' are O. 12. 2 1 3-2 and 3-8 Objectives To recognize conditions that result in parallel lines a To construct parallel lines To construct perpendicular lines a r 13. q 21 b c 19. a p 120 y You can construct the line parallel to a given line through a given point not on the line. You can also construct the perpendicular to a given line at a given point on the line or through a given point not on the line. x 2 Algebra Find the value of x for which < n m. ᐉ 18. m 16. 20 130 ᐉ (2x 10) m 17. ᐉ 24 (3x 20) m (5x 32) Use the segments at the right for Exercises 18 and 19. b 3-3 Objective To relate parallel and perpendicular lines 20. If 2 lines are ' to the same line, then the lines are n (Thm. 3-10). 3-4 Objectives To classify triangles and find the measures of their angles To relate exterior angles to the angles of a triangle a 18. Construct a rectangle with side lengths a and b. See left. 19. Construct a quadrilateral with one pair of parallel opposite sides, each side of length 2a. See margin. b If two lines are perpendicular to the same line, then the two lines are parallel. If a line is perpendicular to one of two parallel lines, then it is perpendicular to both lines. Both of these statements are true only if the lines are coplanar. Use the diagram at the right for Exercises 20 and 21. State the theorem that justifies each statement. a b c 20. If b ' c and b ' d, then c 6 d. d 21. If c 6 d, then a ' c. If a line is ' to one of two n lines, then it is also ' to the other (Thm. 3-11). The sum of the measures of the angles of a triangle is 180. The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. Find the values of the variables. Then classify each triangle by its sides and angles. x 45; y 45; x 60; y 60; equilateral, 22. 23. 24. isosc., right acute x x 60 8 5 78 41 7 61; scalene, acute 190 1 2 105 w 65 (3x 5) 190 x 125 Two lines cut by a transversal are parallel if corresponding angles are congruent, alternate interior angles are congruent, or same-side interior angles are supplementary. 15. 20 a 14. z Chapter 3 Chapter Review x y 120 y 135 Geom_3eTE.03EM.X_189-193 3/24/06 11:13 AM Page 191 Alternative Assessment Name In each of Exercises 25–28, the measures of the three angles of a triangle are given. Find the value of x and then classify the triangle by its angles. Class L4 Date Alternative Assessment Form C Chapter 3 TASK 1 25. x + 10, x - 20, x + 25 55; acute a. Finish labeling the figure, given the following: lines a and b are cut by transversal t; ⬔3 and ⬔8 are same-side interior angles; ⬔4 and ⬔6 are corresponding angles, as are ⬔7 and ⬔3; and ⬔5 and ⬔3 are alternate interior angles. 26. x, 2x, 3x 30; right 1 2 4 3 b. Name three different conditions, each involving ⬔8 and another angle, any one of which is sufficient to guarantee that a 6 b. 27. 20x + 10, 30x - 2, 7x + 1 3; acute 28. 10x - 3, 14x - 20, x + 3 8; obtuse 29. In a right triangle, what is always true about the angles? One l is 90; the remaining 2 ' are comp. c. If a 6 b and m⬔1 = 105, give the measure of the other seven angles. d. Write a flow proof for the following statement: If ⬔7 and ⬔4 are supplementary, then a 6 b. TASK 2 * ) * ) * ) * ) * ) © Pearson Education, Inc. All rights reserved. Draw AB . Construct PB # AB . Then construct PQ 6 AB . A polygon is a closed plane figure with at least three sides. To name a polygon, start at any vertex and list the vertices consecutively in a clockwise or counterclockwise direction. A polygon is convex if no diagonal contains points outside the polygon. Otherwise, it is concave. 3-5 Objectives To classify polygons To find the sums of the measures of the interior and exterior angles of polygons An equilateral polygon has all sides congruent. An equiangular polygon has all angles congruent. A regular polygon is equilateral and equiangular. Geometry Chapter 3 31 Form C Test The sum of the measures of the angles of an n-gon is (n - 2)180. The sum of the measures of the exterior angles of an n-gon, one at each vertex, is 360. Find the measure of an interior angle and an exterior angle of each regular polygon. 30. a hexagon 31. an octagon 32. a decagon 33. a 24-gon 120; 60 135; 45 144; 36 165; 15 34. What is the sum of the measures of the exterior angles for each polygon in Exercises 30–33? 360 When a linear equation is in slope-intercept form, y = mx + b, the slope m and the y-intercept b are easily identified. When a linear equation is in point-slope form, (y - y1) = m(x - x1), point (x1, y1) and slope m can easily be identified. The equation Ax + By = C, where A and B are not both zero, is in standard form. When a linear equation is in standard form, the x- and y-intercepts are readily found. 35–38. 35. Name the slope and y-intercept of y = 2x - 1. Graph the line. See margin. 3-6 Objectives To graph lines given their equations To write equations of lines 36. Name a point on and the slope of y - 3 = -2(x + 5). Graph the line. Spanish Quarter 1 Test - Forms A, B ELL Name 37. Graph y = 2 12. 38. Graph 3x - 4y = 12. 39. Write an equation for the vertical line that contains A(6, -9). x 6 Class Date Chapter Test Form A Quarter 1 Test - Forms D, E Chapter 6 Quarter 1 Test — Forms A, B Graph quadrilateral ABCD. Then determine the most precise name for Name Class each quadrilateral. 1. A(2, 3), B(-4, 3), C(-2, 6), D(1, 6) 2. A(1, 2), B(3, 8), C(5, 2), D(3, -4) Quarter 1 Test 3. A(-1, 4), B(2, 4), C(2, 0), D(-1, 0) L2 L3 Date 4. A(0, 6), B(3, 3), C(0, -5), D(-3, 3) Form A Chapters 1–3 Find QV in each parallelogram. 1. Find the next two terms in the sequence. Q 8, … V 5. 1, 2, 3, 5, 6. Q 4 cm a counterexample for the following 2. Provide statement: If the T animal has four legs, U then it is a dog. The slopes of two nonvertical parallel lines are equal. All vertical lines are parallel. 3-7 Objectives 10. Create an isometric drawing from the R foundation drawing. 7. Q T 5 cm * ) All rights reserved. 8. 43. A(-1, 3), B(4, 8), C(-6, 0), D(2, 8) n 42. A(-3, 3), B(0, 2), C(1, 3), D(-2, -6) # * ) 44. Writing For B(4, 8) and D(2, 8), find the slope of BD . Explain why the slope of any horizontal line is zero. 0; the difference of y-coordinates is always zero. Chapter 3 Chapter Review SFront X 36. m 2; point (5, 3) y 3 1 O 3 1 x y 37. 1 (4x 40) 38 (3x) 10. AC = 7x - 15, BD = 4x + 15 y A 2 1 4 2 O x O 1 1x B 1 (2x) 4. Draw a net for the figure. Label the net with its appropriate dimensions. 11. (2x 33) 12. Find the perimeter of the polygon. 3 6 in. x 12. y * ) D 2 7 (2x) C 24 13. (3x) 10 10 in. 13 x 3 14 34 5. Find the slope of a (3x lineparallel 10) to AB with A(4, 6) and B(-3, 8). 13. Find the measure of ⬔TQM. R 6. Find value of xfor if AC =D 16.and E without using any new variables. Give thethe coordinates points the 2 coordinates 5x 10 of the midpoint of DE. Then 3x find x 4) A B C Q 14. rectangle (3 15. isosceles trapezoid T (2x 16. rhombus 9) 7. Find the value of x. M G (a, c) E (4x 10) D E (3x 5) F (b, 0) D 8. Construct the perpendicular bisector of LM. L D F (a, b) E the 14. Writing Write a paragraph proof for following statement: C (a, 0) If 2x + 4 = 6, then x = 1. B (0, b) G (a c, 0) 15. Find the intersection of planes ABC and LMO. L M A Geometry Chapterjustifies 6 9. What property the following statement? If 4x + 6 = 20, then 4x = 14. C B Form A Test 27 MO 191 Geometry Chapters 1–3 38. y V 110 Quarter 1 Test 35. m 2; y-int. 1 z 2m 11. Find the measure of ⬔1. 9. 2 in. Determine whether AB and CD are parallel, perpendicular, or neither. neither 40. A(-1, -4), B(2, 11), C(1, 1), D(4, 10) 41. A(2, 8), B(-1, -2), C(3, 7), D(0, -3) n © Pearson Education, Inc. All rights reserved. * ) To relate slope and perpendicular lines U Right Find the values of the variables for each figure. © Pearson Education, Inc., publishing as Pearson Prentice Hall. To relate slope and parallel lines 1 31in. 3. Classify the triangle by its angles. The product of the slopes of two nonvertical perpendicular lines is -1. In a plane, every vertical line is perpendicular to every horizontal line. 2 4 in. V 39 y O 2 4 x 2 2 4 191