Common Core Readiness ssessment 3 1. B 3. Find the value of x. D E 2y24 y15 C y13 2x If you know that DE y C, and that D and E are midpoints, which of the following justifies that C 5 2DE? Triangle Midsegment Theorem B Median-ltitude Theorem C Corresp. parts of > n s are > D Definition of triangle bisector 3 B 6 C 7 D 12 4. SU, RW, and VT are medians. Find the length of XT. 2. Find the measure of angle MNQ. M N 12 F 60 G 80 H 100 J 120 100 R 6 Q R V 16 F 9 H 16 G 14 J 18 5. What is the point of concurrency of the lines containing the altitudes of a triangle? circumcenter B incenter C orthocenter D centroid 9 7 U X S W T Copyright by earson Education, Inc., or its affiliates. ll Rights Reserved. 43
6. Which of the following can be used to inscribe a circle in a triangle? F circumcenter G incenter H orthocenter J centroid 7. What is the center of a circle circumscribed about a triangle with vertices (22, 2) (2, 22), and (6, 2)? (2, 2) B (2, 0) C (0, 2) D (0, 0) 9. Given: Lines m and n intersect in point. rove: Lines m and n are coplanar. Which of the following could be a statement in the indirect proof? Lines m and n do not intersect in point. B Lines m and n are not coplanar with point. C Since lines m and n are not in the same plane, they do not share common points. D Since lines m and n do not share common points, they are not coplanar. 8. Suppose you are asked to complete the following indirect proof. Given: n is negative. rove: n 2 is positive. Which of the following is the assumption in the indirect proof? F n is positive. G n 2 is negative. H n is any real number. J n is neither positive nor negative. 10. Given: nbc is an isosceles triangle and m/ 5 90. rove: / is the vertex angle. Which of the following could be a statement in the indirect proof? F By the definition of base angles of an isosceles triangle, / > /B. G By the definition of base angles of an isosceles triangle, /B > /C. H If / > /B, then m/ 1 m/b 1 m/c, 180. J If / > /B, then m/ 1 m/b 1 m/c 5 180. Copyright by earson Education, Inc., or its affiliates. ll Rights Reserved. 44
11. In a field, Raja, Mary, and Miguel are standing in the shape of a triangle. Raja is 128 feet from Mary, and Mary is 143 feet from Miguel. Which of the following is a possible distance between Raja and Miguel? 153 feet B 271 feet C 288 feet D 307 feet 12. On a map, Meridian, Birmingham, and Montgomery form a triangle. Meridian is 109 miles from Birmingham and Birmingham is 91 miles from Montgomery. Which of the following is not a possible distance between Montgomery and Meridian? F 18 miles G 25 miles H 135 miles J 199 miles 13. The lengths of two sides of a triangle are 4 and 7. Give all possible lengths for the third side if the lengths of the sides are all integers. 6, 7, 8, 9, 10, 11, 12 B 3, 4, 5, 6, 7, 8 C 5, 6, 7, 8 D 4, 5, 6, 7, 8, 9, 10 14. What is the sum of the measures of the interior angles of the figure below? M Q F 900 G 720 H 540 J 360 15. The measure of each interior angle of a regular 12-sided polygon is 9. 148 B 150 C 152 D 180 16. Figure BCDEF is a regular hexagon. What is the measure of /EFG? F 40 G 60 H 90 J 120 B C N D F O E G Copyright by earson Education, Inc., or its affiliates. ll Rights Reserved. 45
Use the given coordinates to prove the most precise name for each quadrilateral. 17. B23,1B, 0,5B, L4,2B, K1,22B square B parallelogram C rectangle D rhombus 18. Q1,1B, U2,24B, 23,23B, D24,2B F parallelogram G square H rhombus J rectangle 20. Which of the following would prove that quadrilateral QRST is a parallelogram? T Q F QR > ST G QR y ST H Q > S and T > R J Two pairs of sides are congruent. 21. In ntri, M and D are midpoints of IT and IR, respectively. Which can be proven true? S R 19. C4,23B, D0,25B, E23,1B, F1,3B parallelogram B square C rectangle D rhombus The measure of angle T is equal to the measure of angle R. B MD 5 a 1 2 btr C IM 5 a 1 2 bir D IT > IR Copyright by earson Education, Inc., or its affiliates. ll Rights Reserved. 46
22. Which additional piece of information would prove that quadrilateral WXYZ shown below is a parallelogram? W Z F W > Y G WZ > XY H /WX > /ZY J m/wx 1 m/yx 5180 X Y 24. Use the given coordinates to classify the triangle and find its perimeter. S1,26B, 6,26B, U3,22B F acute isosceles; 5 15 G acute isosceles; 5 10 1 2"5 H acute scalene; 5 10 1 2"5 J acute scalene; 5 15 25. rcs of congruent circles were constructed from the endpoints of XY, intersecting at points and B as shown. What is true about any point on B g in this construction? 23. The values for which ordered pair will show that MTH is a parallelogram? a26, 1 4 b B 1,1B C 4,27B D 3,22B nxy will be an acute isosceles triangle. B nxy will be an equilateral triangle. C will be on the perpendicular bisector of XY. D will be equidistant from and B. 26. Which of the following statements is NOT true? F The diagonals of a rhombus are perpendicular to each other. G The diagonals of a kite are perpendicular to each other. H The diagonals of a kite bisect each other. J The diagonals of a parallelogram bisect each other. Copyright by earson Education, Inc., or its affiliates. ll Rights Reserved. 47
27. The coordinates of three vertices of a parallelogram are (0, 0), (8, 5), and (15, 7). Which of the following is a possible fourth vertex? (27, 22) B (23, 28) C (23, 12) D (7, 2) 29. Find the midpoint of the midsegment of the trapezoid if 5 (4s, 4t), B 5 (4u, 4t), and C 5 (4v, 0). y B (0, 0) C x 28. The figure shown is a kite. What is the x-coordinate of point? (a, 1) (a 4, 1) (t 1 u 1 v, t) B (s 1 u 1 v, 2t) C (u 1 2v, 2t) D (2s 1 2u, 2t 1 2t) F a 2 1 4 G a 1 4 2 H a 1 2 J 2a 1 4 30. Quadrilateral JKLM has vertices J(24, 21), K(21, 2), and L(6, 2). For what coordinates of point M is JKLM a parallelogram? F (3, 22) G (3, 21) H (4, 0) J (4, 21) STO Copyright by earson Education, Inc., or its affiliates. ll Rights Reserved. 48