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Geometry: Chapter 6 Study Guide 1. In the rhombus, What are The diagram is not to scale. | 1 | 1 24º 3 3 | | 2 2 2. In the parallelogram, Find to scale. and The diagram is not 5. In quadrilateral ABCD, and . For what value of x is ABCD a rhombus? A J B K O D M L 6. The sum of the angle measures of a polygon with s sides is 2340. Find s. 3. Find AM in the parallelogram if PN =15 and AO = 6. The diagram is not to scale. M C 7. Find the missing values of the variables. The diagram is not to scale. N 119° x° 106° y° A P O 74° 8. What is LM? A 4. Find the measure of the numbered angles in the rhombus. The diagram is not to scale. L D B M C 9. Find to scale. in the kite. The diagram is not 15. In the figure, the horizontal lines are parallel and Find KL and FG. The diagram is not to scale. | D 3 1 | A 17° 14. What is the measure of one angle in a regular 30-gon? 2 M B A H 8.7 B G || || L K C C J F 8.6 D E 10. How many sides does a regular polygon have if each exterior angle measures 30? 11. In the parallelogram, Find scale. and The diagram is not to A P E D C 17. ABCD is a parallelogram. If then The diagram is not to scale. R A 12. LMNO is a parallelogram. If NM = x + 5 and OL = 2x + 3, find the value of x and then find NM and OL. O B Q O S 16. In quadrilateral ABCD, and . For what value of x is ABCD a rectangle? B N D L M 13. What is the most precise name for quadrilateral ABCD with vertices A(–5, 2), B(–3, 5), C(4, 5), and D(2, 2)? C 18. Find the values of the variables and the lengths of the sides of this kite. y–3 | x+ 2 || || | 2x + 2 x + 11 19. Based on the information given, can you determine that the quadrilateral must be a parallelogram? Explain why or why not. Given: and X Y N W Z 20. For the parallelogram, if find scale. 3 2 and The diagram is not to K L N M 4 1 21. In rectangle KLMN, KM = and LN = 64. Find the value of x. 22. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain why or why not. 23. Find the value of x. The diagram is not to scale. A B (3x + 10)º 148º (x)º D C 27. 112º What is the value of x? A B 24. Find the values of a and b. The diagram is not to scale. L a° M 109° D 65° b° C 28. In the rhombus, Find the value of each variable. The diagram is not to scale. | | 25. In rectangle PQRS, PR = 18x – 28 and QS = x + 380. Find the value of x and the length of each diagonal. P Q 3 1 | | 2 S R 26. ABCD is a parallelogram. If then The diagram is not to scale. 29. What is the sum of the angle measures of a 35-gon? 30. JKLM. If are base angles of isosceles trapezoid and 31. If find so that quadrilateral ABCD is a parallelogram. The diagram is not to scale. A 36. This jewelry box has the shape of a regular pentagon. It is packaged in a rectangular box as shown here. The box uses two pairs of congruent right triangles made of foam to fill its four corners. Find the measure of the foam angle marked. B D C 32. Parallelogram ABCD has the angle measures shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain. x 37. 66º 66º and diagram is not to scale. Find The R | 66º 66º x | U S 34. DEFG is a rectangle. DF = 5x – 3 and EG = x + 5. Find the value of x and the length of each diagonal. 35. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to scale. A B || || 33. A road sign is in the shape of a regular pentagon. What is the measure of each angle on the sign? Round to the nearest tenth. T 38. Find . The diagram is not to scale. 96° 118° 115° 3x – 14 y + 11 104° A 4y – 7 x+ 2 D C 39. In the figure, the horizontal lines are parallel and Find JM. The diagram is not to scale. M A 9 L K J B C D 40. Find the sum of the measures of the angles of the figure. 41. Find the values of the variables in the parallelogram. The diagram is not to scale. 31 96 y° z° x° Geometry: Chapter 6 Study Guide Answer Section 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 120 6 4 15 x = 93, y = 74 88 12 sides 64 x = 2, NM = 7, OL = 7 parallelogram 168 KL = 8.7, FG = 8.6 12 123 x = 9, y = 14; 11, 20 Yes; diagonals of a parallelogram bisect each other. 164 4 Yes; the diagonals bisect each other. 45 x = 24, PR = 404, QS = 404 63 35 x = 6, y = 84, z = 3 5940 154 134 Parallelogram ABCD is a rhombus, because the diagonal bisects two angles. 108 x = 2, DF = 7, EG = 7 x = 8, y = 6 72° 20 73 27 540