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1 Topic 1 eview TOPI VOULY Ě FXWH ULJKW WXVH VWULJKW JOHV p. 17 Ě FJUXHW JOHV p. 16 Ě PHVXUH I JOH p. 17 Ě VLGHV I JOH p. 16 Ě FJUXHW VHJPHWV p. 10 Ě PLGSLW p. 11 Ě VSFH p. 4 Ě GMFHW JOHV p. 22 Ě FVWUXFWL p. 27 Ě SHUSHGLFXOU LVHFWU p. 27 Ě VWULJKWHGJH p. 27 Ě JOH p. 16 Ě FUGLWH p. 10 Ě SHUSHGLFXOU OLHV p. 27 Ě VXSSOHPHWU\ Ě JOH LVHFWU p. 22 Ě FSOU p. 4 Ě SLW OLH SOH p. 4 Ě FOOLHU SLWV p. 4 Ě GLVWFH p. 10 Ě SVWXOWH [LP p. 4 Ě YHUWH[ I JOH p. 16 Ě FPSOHPHWU\ JOHV p. 22 Ě GLJO p. 36 Ě U\ SSVLWH U\V p. 5 Ě YHUWLFO JOHV p. 22 Ě FPSVV p. 27 Ě LWHUVHFWL p. 4 Ě VHJPHW p. 5 Ě FFYH FYH[ p. 36 Ě OLHU SLU p. 22 Ě VHJPHW LVHFWU p. 11 JOHV p. 22 heck Your Understanding hoose the correct term to complete each sentence. 1. ray that divides an angle into two congruent angles is a(n)?. 2.? are two lines that intersect to form right angles. 3. (n)? is a geometric figure drawn using a straightedge and a compass. 1-1 Points, Lines, and Planes point indicates a location and has no size. Use the figure below for 4 6. line is represented by a straight path that extends in two opposite directions without end and has no thickness. 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. Segments:,,, and ays:, or, or,, and 5. Name the intersection of planes and TS. 6. Name three noncollinear points. Points and lines in the same plane are coplanar. Segments and rays are parts of lines. 4. Name two intersecting lines. T S etermine whether the statement is true or false. xplain your reasoning. 7. Two points are always collinear. 8. LM and ML are the same ray. PearsonTXS.com 37

2 1-2 Measuring Segments The distance between two points is the length of the segment connecting those points. Segments with the same length are congruent segments. midpoint of a segment divides the segment into two congruent segments. re and congruent? = =0-50 = 5 =0-7 - (-2)0 =0-50 = 5 =, so For 9 and 10, use the number line below. 9. Find two possible coordinates of such that P = Find the coordinate of the midpoint of PH. 11. Find the value of m. 3m 5 4m If XZ = 50, what are XY and YZ? P H a a 8 X Y Z 1-3 Measuring ngles 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. ngles with the same measure are congruent angles. lassify each angle as acute, right, obtuse, or straight If mjo = 47 and mjo = 73, find mjo. Use the diagram below for 15 and 16. N M P O m O = m O + m O = = If m M = 61 and m MP = 25, find m P. 16. If m NM = 2x + 8 and m P = x + 22, find the value of x. 38 Topic 1 eview

3 1-4 xploring ngle Pairs Some pairs of angles have special names. Name a pair of each of the following. djacent angles: coplanar angles with a common side, a common vertex, and no common interior points Vertical angles: sides are opposite rays omplementary angles: measures have a sum of 90 Supplementary angles: measures have a sum of complementary angles 18. supplementary angles 19. vertical angles 20. linear pair F Linear pair: adjacent angles with noncommon sides as opposite rays ngles of a linear pair are supplementary. Find the value of x. 21. (3x 31) (2x 6) re j and j vertical angles? xplain. No. They have only one set of sides with opposite rays x (4x 15) 1-5 asic onstructions onstruction 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. 24. Use a protractor to draw a 60 angle. Then construct the bisector of the angle. onstruct congruent to F. Step 1 raw a ray with endpoint. Step 2 Open the compass to the length of F. Keep that compass setting and put the compass point on point. raw an arc that intersects the ray. Label the point of intersection. F 25. Sketch LM on paper. onstruct a line segment congruent to LM. Then construct the perpendicular bisector of your line segment. L 26. a. Sketch on paper. onstruct an angle congruent to. b. onstruct the bisector of your angle from part (a). M PearsonTXS.com 39

4 Topic 1 TKS umulative Practice Multiple hoice ead each question. Then write the letter of the correct answer on your paper. 1. Points,,,, and are collinear. is to the right of, is to the right of, and is to the left of. Which of the following is NOT a possible arrangement of the points from left to right?.,,,,.,,,,.,,,,.,,,, 2. Which postulate most closely resembles the ngle ddition Postulate? F. uler Postulate G. Protractor Postulate H. Segment ddition Postulate J. rea ddition Postulate 3. What is the coordinate of the point that is 1 4 the distance from 20 to 4 on a number line? Given: What is the second step in constructing the angle bisector of? F. raw. G. From points and, use the same compass setting to draw arcs that intersect at. H. raw a line segment connecting points and. J. From point, draw an arc that intersects the sides of the angle at points and. 5. Which construction requires drawing only one arc with a compass?. constructing congruent segments. constructing congruent angles. constructing the perpendicular bisector. constructing the angle bisector 6. What is the intersection of < and plane? F. point H. point G. point J. point 7. If and are supplementary angles, what angle relationship between and NNOT be true?. and are right angles.. and are adjacent angles.. and are complementary angles.. and are congruent angles. 8. Which geometric term is undefined? F. plane G. angle bisector H. construction 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? Topic 1 TKS umulative Practice

5 10. If m J = 7y + 2 and m J = 2y + 7, find the value of y. F. y = 3 G. y = 8 H. y = 5 J. y = Which statement is true?. It is possible for three points to be noncoplanar.. plane containing two points of a line contains the entire line.. omplementary angles are congruent.. straight angle has a supplement. Gridded esponse 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? X K J 2b 1 Y 26 4b 15. The sum of the measures of a complement and a supplement of an angle is 200. What is the measure of the angle? 16. In, the coordinate of point is -4, and the coordinate of point is 6. What is the coordinate of a point such that is 3 8 of the distance from point to point? 17. < VW is the bisector of Y, and they intersect at. If Y = 3.5, what is Y? Z onstructed esponse 18. opy the graph below. Find the midpoints of two adjacent sides of the square. onnect the perpendicular bisectors of the two adjacent sides. What is the perimeter of the new square? Show your work. 6 x 4 2 O Suppose P =. Your friend says that is always the midpoint of P. Is he correct? xplain. 20. Why might it be useful to have more than one way to name an angle? 21. The bisector of obtuse O goes through point. The bisector of O goes through point. a. If m O = 4x + 12, what is the measure of O in terms of x? How do you know? b. If m O = 4x + 12 and m O = 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? xplain. 4 2 y PearsonTXS.com 41