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Review Chapter 6 - Geometry A Short Answer 1. Find the values of the variables and the lengths of the sides of this kite. x +| 3 || || y–3 | 2x + 5 x+ 6 2. ABCD is a parallelogram. If A D then The diagram is not to scale. B C 3. LMNO is a parallelogram. If NM = x + 35 and OL = 4x + 8 find the value of x and then find NM and OL. O N L M 4. Find the values of the variables in the parallelogram. The diagram is not to scale. 5. In the parallelogram, and J Find The diagram is not to scale. K O L M 6. Find AM in the parallelogram if PN =14 and AO = 6. The diagram is not to scale. M N A P 7. If O find so that quadrilateral ABCD is a parallelogram. The diagram is not to scale. A B D C Find the value of each variable. The diagram | | 8. In the rhombus, is not to scale. 3 1 | | 2 9. DEFG is a rectangle. DF = 3x – 5 and EG = x + 3. Find the value of x and the length of each diagonal. 10. Find the values of a and b.The diagram is not to scale. a° 48° 123° b° 11. The isosceles trapezoid is part of an isosceles triangle with a 44° vertex angle. What is the measure of an acute base angle of the trapezoid? Of an obtuse base angle? The diagram is not to scale. 12. are base angles of isosceles trapezoid JKLM. If 13. and Find The diagram is not to scale. R | | S || || U T 14. Find a counterexample to show that the conjecture is false. Conjecture: Any number that is divisible by 2 is also divisible by 4. 15. Find the values of x and y. The diagram is not to scale. (x – 1)° 53° (y – 9)° 65° and 16. The two triangles are congruent as suggested by their appearance. Find the value of d. The diagrams are not to scale. d° 43° g 17 b f° e° 15 47° 8 c 17. Justify the last two steps of the proof. Given: and Prove: E F G H Proof: 1. 2. 3. 4. 1. Given 2. Given 3. 4. 18. Find the length of the midsegment. The diagram is not to scale. 33 42 6x + 5 42 33 3x + 46 19. bisects Find the value of x. The diagram is not to scale. | E | 8x + 20 F ) 9x ) 21° D 20. G Find 1 4 2 3 Drawing not to scale 21. Find the values of the variables and the lengths of the sides of this rectangle. The diagram is not to scale. 10x 2x + 8 10y 16y + 28 22. What type of quadrilateral has two pairs of parallel sides? 23. Isosceles trapezoid ABCD has legs 14, find the value of y. and and base If AB = 5y – 3, BC = 3y – 3, and CD = 6y – 24. Give the name that best describes the parallelogram and find the measures of the numbered angles. The diagram is not to scale. | 4 | | 3 1 2 100ο | 25. Judging by appearance, classify the figure in as many ways as possible using rectangle, trapezoid, square, quadrilateral, parallelogram, rhombus. Review Chapter 6 - Geometry A Answer Section SHORT ANSWER 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. x = 1, y = 7; 4, 7 118 x = 9, NM = 44, OL = 44 104 6 134 x = 6, y = 84, z = 15 x = 4, DF = 7, EG = 7 68°; 112° 154 60 18 x = 66, y = 71 43 Reflexive Property of ; SSS 29 20 57 x = 6, y = 2; 20, 60 parallelogram 11 Rhombus; the measure of all numbered angles equal 42. quadrilateral