By Mary Behr Altieri

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DE + EF = DF _ DE + 2 3 = 12 4 3 3 3 DE + 2_ - 2_ = 12 - 2_ 4 4 4 1 DE = 9_ 4 E 2 34 in. F 12 in. Betweenness of points Substitution Subtract 2_ from each side. 3 4 1 inches long. So, DE is 9 _ 4 c. Find y and QP if P is between Q and R, QP = 2y, QR = 3y + 1, and PR = 21. 3y ϩ 1 2y Q 21 P R Draw a figure to represent this information. QR = QP + PR Betweenness of points 3y + 1 = 2y + 21 Substitute known values. 3y + 1 - 1 = 2y + 21 - 1 Subtract 1 from each side. 3y = 2y + 20 3y - 2y = 2y + 20 - 2y y = 20 Simplify.

Point T is on line m. Point T is on line . y Q x P B A R N Line x and point R are in N. Point R lies in N. Plane N contains R and line x. Line y intersects N at R. Point R is the intersection of line y with N. Lines y and x do not intersect. AB is in P and Q. Points A and B lie in both P and Q. Planes P and Q both contain AB . Planes P and Q intersect in AB . AB is the intersection of P and Q. Reading to Learn Write a description for each figure. 1. T ᐉ P Q 2. j R G 3. H X 4. Draw and label a figure for the statement Planes A, B, and C do not intersect.

A AB = 4n −− B The midpoint of AB is (2n, 2n). C AB = n √8 −− D The midpoint of AB is (4n, 10n). 3. SR = 3x, RT = 2x + 1, ST = 6x ‒ 1 4. SR = 5x ‒ 3, ST = 7x + 1, RT = 3x - 1  and XT  are opposite rays. In the figure, XP (Lesson 1-4) R S Find the coordinates of the midpoint of each segment. Then find the distance between the endpoints. (Lesson 1-3) 5. Q T P y B (–4, 3) X 13. If m∠SXT = 3a ‒ 4, m∠RXS = 2a + 5, and m∠RXT = 111, find m∠RXS. x O A (3, –1) 14. If m∠QXR = a + 10, m∠QXS = 4a ‒ 1, and m∠RXS = 91, find m∠QXS.

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