Polygons and Quadrilaterals
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1 Chapter Test Form B Circle the best answer. 1. Which best describes the figure? 6. In JKLM, what is the value of m K? A regular convex heptagon B irregular convex heptagon C irregular concave heptagon D irregular convex hexagon 2. What is the measure of each interior angle in a regular convex nonagon? F 40 H 180 G 140 J What is the value of a? F 15 H 65 G 57 J QR ST. Which additional information is NOT enough to conclude that QRST is a parallelogram? A RS QT C QR ST B RS QT D Q S 8. Which of the quadrilaterals MUST be parallelograms? A 2 C 180 B 90 D Not here 4. The diagonals of ABCD intersect at X. Which is always true? F BX G AX XD XB H A D J m A m C In DEFG, what is EG? A 25 C 50 B 30 D Not here F A only G B only 9. Which is NOT always true? H Neither A nor B J Both A and B A The diagonals of a rectangle divide the rectangle into four nonoverlapping isosceles triangles. B The diagonals of a square divide the square into four nonoverlapping right triangles. C The longer diagonal of a rhombus is perpendicular to two sides of the rhombus. D The sum of the lengths of the diagonals of a rhombus is less than the perimeter of the rhombus.
2 Chapter Test Form B continued 10. WXYZ is a rectangle. Which is NOT an expression for WT? 14. In kite UVWX, m XUV 84, and m WVX 68. What is m VWX? F 5x 18 H 10x 12 G 7x 6 J 12x Which set of numbers could be the measures of DAB, ACB, and DBC, respectively? F 22 H 44 G 42 J GE 5x 2 and DF 8x 7. What is GE? A 114, 57, 32.5 B 115, 32.5, 57.5 C 116, 57.5, 32.5 D 117, 58.5, What additional information would allow you to conclude that JKLM is a rhombus? A 16 B 17 C 18 D In trapezoid PQRS, if YX is the midsegment, what could be the lengths of PQ and SR? F JK ML and JM KL. G JM JK H JL and MK bisect each other. J JL MK 13. Which is the best name for the quadrilateral with vertices at (2, 2), (5, 2), (1, 5), and ( 2, 1)? A parallelogram C rhombus B rectangle D square F 4 cm and 8 cm G 9 cm and 15 cm H 17 cm and 31 cm J 18 m and 30 m
3 Chapter Test Form B 1. Name the polygon by its number of sides and tell whether it is regular or irregular. 7. Write True or False. The quadrilateral must be a parallelogram. 2. Find the measures of each interior angle of a regular octagon. 8. Show that JKLM is a parallelogram for x 7 and y Find the value of a. 4. Write a biconditional statement to define the term parallelogram. 5. ABCD is a parallelogram. Find AB and BX. 9. Complete the sentence. A is a parallelogram that has the properties of both a and a. 6. EFGH is a parallelogram. Find m E. 10. ABCD is a rectangle with diagonals BD and AC that intersect at X. BD 12x 6 inches and AX 4x 5 inches. Find DX.
4 Chapter Test Form B continued 11. RSTQ is a rhombus. Find m PST. 14. In kite JKLM, m LMN 25, and m LKN 43. Find m MLK. 12. Given: WXYZ is a parallelogram. WY and XZ bisect each other and WY XZ. Conclusion: WXYZ is a rectangle. Determine whether the conclusion is valid. If not, tell why not. 15. In trapezoid ABCD, find m A. 16. XY is the midsegment of trapezoid ABCD. Find AB. 13. Tell whether the parallelogram is a rectangle, rhombus, or square.
5 Chapter Test Form B: Multiple Choice 1. C 9. C 2. G 10. J 3. A 11. D 4. F 12. G 5. C 13. D 6. H 14. H 7. B 15. B Chapter Test Form B: Free Response 1. irregular hexagon A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides. 5. AB 30; BX True 8. m J (9y 1) [9(14) 1] 127 ; m L (10y 13) [10(14) 13] 127 ; m K (7x 4) [7(7) 4] 53 ; Since , K is supplementary to both J and L. JKLM is a parallelogram by Theorem square; rhombus; rectangle in Not valid; possible answer: conditions for a rectangle are 1 of a is a rt. or the diagonals of a are. While the quadrilateral is a and a rhombus, neither of the conditions for a rectangle are met. 13. Sample answer: 5 ( 5) The diagonals are congruent so by Theorem 6-5-2, DEFG is a rectangle. slope of slope of DF EG 1 (1) 1, 7 to EG ( 5) ( 4) 5 so DF is not perpendicular So DEFG is not a rhombus and therefore cannot be a square. DEFG is a rectangle DF [2 ( 5)] + (1 0) EG [1 ( 4)] [( 2) 3]
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