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Topic 1 Review TOPIC VOCABULARY Ě DFXWHULJKWREWXVHVWUDLJKW DQJOHV p. 17 Ě FRQJUXHQWDQJOHV p. 16 Ě PHDVXUHRIDQDQJOH p. 17 Ě VLGHVRIDQDQJOH p. 16 Ě FRQJUXHQWVHJPHQWV p. 10 Ě PLGSRLQW p. 11 Ě VSDFH p. 4 Ě DGMDFHQWDQJOHV p. 22 Ě FRQVWUXFWLRQ p. 27 Ě SHUSHQGLFXODUELVHFWRU p. 27 Ě VWUDLJKWHGJH p. 27 Ě DQJOH p. 16 Ě FRRUGLQDWH p. 10 Ě SHUSHQGLFXODUOLQHV p. 27 Ě VXSSOHPHQWDU\ Ě DQJOHELVHFWRU p. 22 Ě FRSODQDU p. 4 Ě SRLQWOLQHSODQH p. 4 Ě FROOLQHDUSRLQWVp. 4 Ě GLVWDQFH p. 10 Ě SRVWXODWHD[LRP p. 4 Ě YHUWH[RIDQDQJOH p. 16 Ě FRPSOHPHQWDU\DQJOHV p. 22 Ě GLDJRQDO p. 36 Ě UD\RSSRVLWHUD\V p. 5 Ě YHUWLFDODQJOHV p. 22 Ě FRPSDVV p. 27 Ě LQWHUVHFWLRQ p. 4 Ě VHJPHQW p. 5 Ě FRQFDYHFRQYH[ p. 36 Ě OLQHDUSDLU p. 22 Ě VHJPHQWELVHFWRU p. 11 DQJOHV p. 22 Check Your Understanding Choose the correct term to complete each sentence. 1. A ray that divides an angle into two congruent angles is a(n) ? . 2. ? are two lines that intersect to form right angles. 3. A(n) ? is a geometric figure drawn using a straightedge and a compass. 1-1 Points, Lines, and Planes Quick Review Exercises A point indicates a location and has no size. Use the figure below for Exercises 4–6. A line is represented by a straight path that extends in two opposite directions without end and has no thickness. A plane is represented by a flat surface that extends without end and has no thickness. Points that lie on the same line are collinear points. Name all the segments and rays in the figure. A Segments: AB, AC, BC, and BD > > > > > > > Rays: BA , CA or CB , AC or AB , BC , and BD 5. Name the intersection of planes QRB and TSR. 6. Name three noncollinear points. Points and lines in the same plane are coplanar. Segments and rays are parts of lines. Example 4. Name two intersecting lines. T S Q R C D A B Determine whether the statement is true or false. Explain your reasoning. 7. Two points are always collinear. > > 8. LM and ML are the same ray. D B C PearsonTEXAS.com 37 1-2 Measuring Segments Quick Review Exercises The distance between two points is the length of the segment connecting those points. Segments with the same length are congruent segments. A midpoint of a segment divides the segment into two congruent segments. For Exercises 9 and 10, use the number line below. P 24 H 2 0 22 4 9. Find two possible coordinates of Q such that PQ = 5. Example 10. Find the coordinate of the midpoint of PH. Are AB and CD congruent? C 28 A D 26 24 B 0 22 11. Find the value of m. 2 3m 1 5 AB = 0 -3 - 2 0 = 0 -5 0 = 5 4m 2 10 A CD = 0 -7 - ( -2) 0 = 0 -5 0 = 5 B C 12. If XZ = 50, what are XY and YZ? AB = CD, so AB ≅ CD. a18 a X Z Y 1-3 Measuring Angles Quick Review Exercises Two rays with the same endpoint form an angle. The endpoint is the vertex of the angle. You can classify angles as acute, right, obtuse, or straight. Angles with the same measure are congruent angles. Classify each angle as acute, right, obtuse, or straight. 13. 14. Example If mjAOB = 47 and mjBOC = 73, find mjAOC. B A Use the diagram below for Exercises 15 and 16. N M P O m∠AOC = m∠AOB + m∠BOC = 47 + 73 = 120 38 Topic 1 Review C Q R 15. If m∠MQR = 61 and m∠MQP = 25, find m∠PQR. 16. If m∠NQM = 2x + 8 and m∠PQR = x + 22, find the value of x. 1-4 Exploring Angle Pairs Quick Review Exercises Some pairs of angles have special names. Name a pair of each of the following. r Adjacent angles: coplanar angles with a common side, a common vertex, and no common interior points 17. complementary angles r Vertical angles: sides are opposite rays 18. supplementary angles r Complementary angles: measures have a sum of 90 19. vertical angles r Supplementary angles: measures have a sum of 180 20. linear pair r Linear pair: adjacent angles with noncommon sides as opposite rays Find the value of x. Angles of a linear pair are supplementary. 21. B A C D E (3x 1 31)8 F (2x 2 6)8 Example E Are jACE and jBCD vertical angles? Explain. A No. They have only one set of sides with opposite rays. 22. B C D 3x8 (4x 2 15)8 1-5 Basic Constructions Quick Review Exercises Construction is the process of making geometric figures using a compass and a straightedge. Four basic constructions involve congruent segments, congruent angles, and bisectors of segments and angles. 23. Use a protractor to draw a 73° angle. Then construct an angle congruent to it. Example Construct AB congruent to EF . E F Step 1 Draw a ray with endpoint A. 25. Sketch LM on paper. Construct a line segment congruent to LM. Then construct the perpendicular bisector of your line segment. M L A 26. a. Sketch ∠B on paper. Construct an angle congruent to ∠B. Step 2 Open the compass to the length of EF . Keep that compass setting and put the compass point on point A. Draw an arc that intersects the ray. Label the point of intersection B. 24. Use a protractor to draw a 60° angle. Then construct the bisector of the angle. b. Construct the bisector of your angle from part (a). A B B PearsonTEXAS.com 39 Topic 1 TEKS Cumulative Practice Multiple Choice Read each question. Then write the letter of the correct answer on your paper. 1. Points A, B, C, D, and E are collinear. A is to the right of B, E is to the right of D, and B is to the left of C. Which of the following is NOT a possible arrangement of the points from left to right? A. D, B, A, E, C C. B, D, E, C, A B. D, B, A, C, E D. B, A, E, C, D 5. Which construction requires drawing only one arc with a compass? A. constructing congruent segments B. constructing congruent angles C. constructing the perpendicular bisector D. constructing the angle bisector < > 6. What is the intersection of AC and plane Q? A 2. Which postulate most closely resembles the Angle Addition Postulate? E B D F. Ruler Postulate Q C G. Protractor Postulate H. Segment Addition Postulate J. Area Addition Postulate 3. What is the coordinate of the point that is 14 the distance from 20 to 4 on a number line? H. point B G. point Q J. point D 7. If ∠A and ∠B are supplementary angles, what angle relationship between ∠A and ∠B CANNOT be true? A. 8 C. 16 A. ∠A and ∠B are right angles. B. 9 D. 15 B. ∠A and ∠B are adjacent angles. C. ∠A and ∠B are complementary angles. 4. Given: ∠A What is the second step in constructing the angle bisector of ∠A? D A D. ∠A and ∠B are congruent angles. 8. Which geometric term is undefined? F. plane B G. angle bisector H. construction C > F. Draw AD . G. From points B and C, use the same compass setting to draw arcs that intersect at D. H. Draw a line segment connecting points B and C. J. From point A, draw an arc that intersects the sides of the angle at points B and C. 40 F. point E Topic 1 TEKS Cumulative Practice J. opposite rays 9. The measure of an angle is 12 less than twice the measure of its supplement. What is the measure of the angle? A. 28 C. 64 B. 34 D. 116 10. If m∠BDJ = 7y + 2 and m∠JDR = 2y + 7, find the value of y. B K J D Constructed Response 18. Copy the graph below. Find the midpoints of two adjacent sides of the square. Connect the perpendicular bisectors of the two adjacent sides. What is the perimeter of the new square? Show your work. R y F. y = 3 G. y = 8 4 H. y = 5 2 J. y = 9 x 11. Which statement is true? 26 24 22 O A. It is possible for three points to be noncoplanar. 22 B. A plane containing two points of a line contains the entire line. 24 C. Complementary angles are congruent. D. A straight angle has a supplement. 12. The measure of an angle is 78 less than the measure of its complement. What is the measure of the angle? 13. The measure of an angle is one third the measure of its supplement. What is the measure of the angle? 14. Y is the midpoint of XZ. What is the value of b? 2b 2 1 26 2 4b Y 19. Suppose PQ = QR. Your friend says that Q is always the midpoint of PR. Is he correct? Explain. 20. Why might it be useful to have more than one way to name an angle? Gridded Response X 4 Z 15. The sum of the measures of a complement and a supplement of an angle is 200. What is the measure of the angle? 21. The bisector of obtuse ∠AOD goes through point C. The bisector of ∠AOC goes through point B. a. If m∠COD = 4x + 12, what is the measure of ∠BOC in terms of x? How do you know? b. If m∠COD = 4x + 12 and m∠AOD = 120, what is the value of x? How do you know? 22. In JK , JH = 4x - 15 and HK = 2x + 3, where H is between J and K on JK . a. If JK = 48, find the value of x. b. Is H the midpoint of JK ? Explain. 16. In AB, the coordinate of point A is -4, and the coordinate of point B is 6. What is the coordinate of a point C such that C is 38 of the distance from point A to point B? < > 17. VW is the bisector of AY , and they intersect at E. If EY = 3.5, what is AY ? PearsonTEXAS.com 41