Common Core Readiness Assessment 3
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1 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 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 R 6 Q R V 16 F 9 H 16 G 14 J 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
2 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/ 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 Copyright by earson Education, Inc., or its affiliates. ll Rights Reserved. 44
3 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, What is the sum of the measures of the interior angles of the figure below? M Q F 900 G 720 H 540 J The measure of each interior angle of a regular 12-sided polygon is B 150 C 152 D 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
4 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
5 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 H acute scalene; "5 J acute scalene; 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
6 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 G a H a 1 2 J 2a 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
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