180-90-52 Key

Key Definitions: write a definition for each quadrilateral and draw a picture showing the properties. 1. Parallelogram - a quadrilateral with both pairs   of opposite sides parallel. 2. Square - a parallelogram with 4 congruent sides and 4 right angles 3. Rectangle - a parallelogram with 4 right angles. 4. Rhombus - a parallelogram with 4 congruent sides 5. Trapezoid - a quadrilateral with exactly one pair of parallel sides. 6. Isosceles Trapezoid - a trapezoid with the non-parallel sides are congruent 7. Kite - a quadrilateral with adjacent sides congruent and no parallel sides Properties: Use the properties of the quadrilateral to find the value of the missing angles or variables. Parallelograms: 8.   y - 4 = 28 y = 32 9. 2x - 4 = 16 2x = 20 x = 10 10. ∠1 = 180 - 47 - 72 = 61° ∠2 = 72° ∠3 = 180 - 72 = 108° ∠4 = 32° 11. 6x - 22 = 4x - 4 2x = 18 x = 9 12. m∠1 = 180 - 110 - 70 = 0° m∠2 = 110° m∠3 = 70° m∠4 = 32° (Alt. Int. ∠s) 13. m∠1 = 150° m∠2 = 30° (Alt. Int. ∠s) m∠3 = 22° m∠4 = 113° Rhombuses: 16. m∠1 = 180 - 54 - 54 = 72° m∠2 = 54° (Thm 6.12) m∠3 = 54° (Thm 6.12) m∠4 = 72° (Thm 6.2) 17. m∠1 = 90° (Thm 6.10) m∠2 = 90° (Thm 6.10) m∠3 = 90° (Thm 6.10) m∠4 = 29° (Thm 6.9) Rectangles: 19. m∠1 = 90 - 72 = 18° (Complementary) m∠2 = 180 - 144 = 36° (Linear Pair) m∠3 = 180 - 18 - 144 = 18° m∠4 = 180 - 18 - 144 = 18° 20. m∠1 = 60 m∠2 = 30 m∠3 = 60 m∠4 = 30 21. m∠1 = 37° m∠2 = 90 - 37 = 53° m∠3 = 106° m∠4 = 180 - 106 - 74 = 0° Trapezoids: 23. 3x - 3 = x + 5 2x = 8 x = 4 24. 7x = 2x + 5 5x = 5 x = 1 25. m∠1 = 180 - 79 - 101 = 0° m∠2 = 79° m∠3 = 101° Kites: 26. x + x + 101 + 48 = 360 2x + 149 = 360 2x = 211 x = 105.5 27. m∠1 = 90° m∠2 = 180 - 90 - 65 = 25° 28. 2x + 10 + 6x + 90 = 180 8x + 100 = 180 8x = 80 x = 10 Name each quadrilateral in as many ways as possible. 1. Kite 2. Trapezoid 3. Rectangle 4. Parallelogram 5. Trapezoid 6. Square Rectangle Parallelogram Rhombus Find the values of the variables, then find the lengths of the sides. 7. 2x - 3 = x + 4 x = 7 8. 2m + 8 = 3m - 1 m = 9 9. 5 + 5 = 5m - 2 5 + 1 = 5m - 2 5 + 1 = 5(9) - 2 5 + 1 = 43 5 = 42 10. 2x + 2 = 4x + 3 2x = 4x + 1 -2x = 1 x = -1/2 Find the value of the variable or the missing angle. 11. 4x - 10 = 3x - 2 x = 8 12. D = 12 13. H = EG x = 9 14. m∠1 = 180 - 80 - 100 = 0° m∠2 = 80° m∠3 = 100°