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6. Give another name for line b. SOLUTION: There are two point S and T marked on the line b. So, the line b can also be called Study Guide and Review Fill in the blank in each sentence with the vocabulary term that best completes the sentence. 1. A _____ is a flat surface made up of points that extends infinitely in all directions. SOLUTION: A plane is a flat surface made up of points that extends infinitely in all directions. Therefore, the correct answer is plane. 7. Name a point that is not contained in any of the three lines a, b, or c. SOLUTION: Here, W is a point on the plane R and is not on any of the lines on the plane. 8. Give another name for plane WPX. SOLUTION: The plane WPX is also named as plane R. 2. A set of points that all lie on the same line are said to be _____. Name the geometric term that is best modeled by each item. SOLUTION: A set of points that all lie on the same line are said to be collinear points. Therefore, the correct answer is collinear. 9. 3. If two lines intersect to form four right angles, the lines are called _____. SOLUTION: In the figure, two flat surfaces intersect each other. The two flat surfaces model two planes. Since the intersection of two planes form a line, the item models a line. SOLUTION: If two lines intersect to form four right angles, the lines are called perpendicular. 4. If the sum of the measures of two angles is 180, then the angles are called _____ angles. SOLUTION: If the sum of the measures of two angles is 180, then the angles are called supplementary angles. Use the figure to complete each of the following. 10. SOLUTION: Each bead denotes a location. So, it models a point. Find the value of the variable and XP, if X is between P and Q. 11. XQ = 13, XP = 5x – 3, PQ = 40 5. Name the intersection of lines a and c. SOLUTION: The lines a and c intersect at the point P. 6. Give another name for line b. SOLUTION: There are two point S and T marked on the line b. So, the line b can also be called 7. Name a point that is not contained in any of the three lines a, b, or c. SOLUTION: eSolutions Manual by the Cognero Here, W is-aPowered point on plane R and is not on any of the lines on the plane. SOLUTION: Here X is between P and Q. So, PQ = XP + XQ. We have XQ = 13, XP = 5x – 3, and PQ = 40. 40 = 13 + 5x – 3 30 = 5x 6=x So, XP = 5(6) – 3 = 27. Page 1 12. XQ = 3k, XP = 7k – 2, PQ = 6k + 16 SOLUTION: 10. SOLUTION: Study Guide and Review Each bead denotes a location. So, it models a point. Find the value of the variable and XP, if X is between P and Q. 11. XQ = 13, XP = 5x – 3, PQ = 40 The distance between points A and B is . 14. P(2, –1) and Q(10, –7) SOLUTION: SOLUTION: Here X is between P and Q. So, PQ = XP + XQ. We have XQ = 13, XP = 5x – 3, and PQ = 40. The distance between P and Q is 40 = 13 + 5x – 3 30 = 5x 6=x or 10. 15. M(9, –2) and N(–1, 4) SOLUTION: So, XP = 5(6) – 3 = 27. 12. XQ = 3k, XP = 7k – 2, PQ = 6k + 16 SOLUTION: Here X is between P and Q. So, PQ = XP + XQ. We have XQ = 3k, XP = 7k – 2, PQ = 6k + 16. The distance between points M and N is . 16. J(3, 2) and K(6, –5) SOLUTION: 6k + 16 = 7k – 2 + 3k 6k – 10k = –2 – 16 –4k = –18 k = 4.5 So, XP = 7(4.5) – 2 = 29.5. Find the distance between each pair of points. 13. A(–3, 1) and B(7, 13) SOLUTION: The distance between J and K is . Find the coordinates of the midpoint of a segment with the given endpoints. 18. L(–3, 16), M (17, 4) SOLUTION: Use the Midpoint Formula . The distance between points A and B is . 14. P(2, –1) and Q(10, –7) SOLUTION: Substitute. The midpoint of eSolutions Manual - Powered by Cognero is (7, 10). Page 2 19. C(32, –1), D(0, –12) Guide and Review Study The distance between J and K is . Find the coordinates of the midpoint of a segment with the given endpoints. 18. L(–3, 16), M (17, 4) SOLUTION: Use the Midpoint Formula The midpoint of is (16, –6.5). Find the coordinates of the missing endpoint if M is the midpoint of 20. X(–11, –6), M (15, 4) SOLUTION: Let the coordinates of Y be (x, y). . Then by the Midpoint Formula, . Substitute. Write two equations to find the coordinates of Y. The midpoint of is (7, 10). 19. C(32, –1), D(0, –12) SOLUTION: Use the Midpoint Formula . Substitute. The coordinates of Y are (41, 14). 21. M (–4, 8), Y(19, 0) The midpoint of is (16, –6.5). Find the coordinates of the missing endpoint if M is the midpoint of 20. X(–11, –6), M (15, 4) SOLUTION: Let the coordinates of Y be (x, y). SOLUTION: Let the coordinates of X be (x, y). Then by the Midpoint Formula, . Write two equations to find the coordinates of X. Then by the Midpoint Formula, . Write two equations to find the coordinates of Y. The coordinates of X are (–27, 16). eSolutions Manual - Powered by Cognero The coordinates of Y are (41, 14). For Exercises 25–28, refer to the figure below. Page 3 SOLUTION: Vertical angles are two nonadjacent angles formed by two intersecting lines. Here, QWP and XWV are a pair of vertically opposite angles. Study Guide and Review The coordinates of X are (–27, 16). For Exercises 25–28, refer to the figure below. 32. If m SXW = 5x – 16, find the value of x so that SOLUTION: Since 25. Name the vertex of That is, 5x – 16 = 90. Add 16 to both sides. 5x = 106 Divide both sides by 5. x = 21.2 7. SOLUTION: Here, 7 is same as the angle CGJ. So, the vertex of the angle is G. 26. Write another name for SOLUTION: Here, 4 is same as the Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular. 4. CDG. 34. 27. Name the sides of 2. SOLUTION: Here, 2 is same as the sides are SOLUTION: The polygon has 3 sides. So, it is a triangle. No line containing any of the sides will pass through the interior of the triangle, so it is convex. All of the sides are congruent, so it is equilateral. All of the angles are congruent, so it is equiangular. Since the polygon is convex, equilateral, and equiangular, it is regular. So this is a regular triangle. ACH. Therefore, its For Exercises 30–32, refer to the figure below. 30. Name an angle supplementary to TVY. SOLUTION: Supplementary angles are two angles with measures that have a sum of 180°. Here, TVR is supplementary to TVY. 35. SOLUTION: The polygon has 12 sides. So, it is a dodecahedron. Four of the lines containing the sides of the polygon will pass through the interior of the dodecahedron, so it is concave. 31. Name a pair of vertical angles with vertex W. SOLUTION: Vertical angles are two nonadjacent angles formed by two intersecting lines. Here, QWP and XWV are a pair of vertically opposite angles. 32. If m SXW = 5x – 16, find the value of x so that SOLUTION: Since eSolutions Manual - Powered by Cognero That is, 5x – 16 = 90. Add 16 to both sides. Only convex polygons can be regular, so this is an Page 4 irregular dodecahedron. interior of the triangle, so it is convex. All of the sides are congruent, so it is equilateral. All of the angles are congruent, so it is equiangular. Since the polygon is convex, equilateral, and equiangular, it is regular. Study Review SoGuide this is and a regular triangle. 35. SOLUTION: The polygon has 12 sides. So, it is a dodecahedron. Four of the lines containing the sides of the polygon will pass through the interior of the dodecahedron, so it is concave. Only convex polygons can be regular, so this is an irregular dodecahedron. eSolutions Manual - Powered by Cognero Page 5