Geometry – Ch 6 Review Quadrilaterals Using the grid, identify which quadrilaterals satisfy the following properties: Property Paraallel- Rectangle Rhombus Square Trapezoid Kite ogram Both pairs of opposite sides are parallel. The diagonals bisect each other. Opposite angles are congruent. Only one pair of parallel sides. Two pair of adjacent congruent sides. The diagonals are perpendicular Opposite sides are congruent. All four sides are congruent. All four angles are right angles. Each diagonal bisects a pair of opposite angles. The diagonals are congruent. Consecutive angles are supplementary. 1. Find the sum of the measures of the interior angles of the convex polygon. Heptagon = _______ 2. Find the measure of each interior and exterior angle in the regular polygon. 45-gon: Interior = _______, Exterior = ________ 3. Given that 120° is the measure of an interior angle of a regular polygon, the number of sides = _______ 4. Given hexagon ABCDEF, find the value of x = _______ and the measure of each angle: mA = ______ mD = ______ mB = ______ mE = ______ mC = ______ mF = ______ 5. OMIT……. For the following problems, 6-9, use the associated figure to answer questions about each quadrilateral. PQRS is a parallelogram. Find the unknown measure(s). 6. If m2 25 and m9 48 , then mSPQ = _____ 7. If PQ = 7x – 3 and SR = 5x + 5, then PQ = ______ 2 8. If ST = 8, then SQ = _____ 9. If mPSR 75 , then mPQR = _____, mQRS = ______ RSTU is a rectangle. Find the unknown measure(s). 10. If m1 9x 3 and m3 7x 5, then m3 = ______ 11. If RV = 4x + 1 and RT = 10x – 2 , then RT = ______ 12. If m11 11x 4 and m7 6x 1, then m7 = ______ 13. If m4 54 , then m5= ______ and m2 = ______ JKLM is a rhombus. Find the unknown measure(s). 14. If MN = 6x – 5 and NK = 4x + 1, then MK = ______ 15. If m10 7x 8, then x = ______ 16. If m6 52 , then mJKL = _____ 17. If KL = 13, then ML = _____, JM = ______, JK = _______ 3 ABCD is a square. Find the unknown measure(s). 18. If AB = 5x + 1 and BC = 8x – 11, then AB = ______, BC = ______, CD = ______, AD = _______ 19. If m3 8x 2 , then x = ______ 20. If AE = 19, then DB = _______ 21. m1 = ______ ABCD is an isosceles trapezoid with median EF. Find the unknown measure(s). 22. If AB = 11 and DC = 23, then EF = _______ 23. If AD = 3x – 2 and BC = x + 6, then AD = ______ 24. If AE = 7, then ED = ______ 25. If m6 43 , then m4 = _____, m5 = _____ and m2 = _____ 4 ABCD is a kite. Find the unknown measure. 26. If AB = 8x – 2, and AD = 6x + 4, then AD = ______ 27. If mCED 7x 6, then x = _____ 28. If mABC 12x 10 and mADC 15x 14 , then mADC = ______ 29. If mBAC 24 , then mDAC = ______ 5 Answers to Chapter 6 Review - 1. 900˚ 2. Int: 172˚ Ext: 8˚ 3. 6 4. x = 18, mA = 108˚, mB = 126˚ mC = 90˚, mD = 144˚, mE= 144˚, mF = 108˚ 5. 60 omit 6. 107˚ 7. 25 8. 16 9. 75˚, 105˚ 10. 33˚ 11. 18 12. 31˚ 13. 72˚, 108˚ 14. 26 15. 14 16. 104˚ 17. 13 18. 21 1. yes 19. 11 2. no 20. 38 3. yes 21. 45˚ 4. no 22. 17 5. concave 23. 10 6. convex 24. 7 7. convex 25. 43˚, 43˚, 137˚ 8. concave 26. 22 9. Sometimes 24. equiangular 27. 12 10. Always 25. regular 28. 106˚ 11. Sometimes 26. none 29. 24˚ 12. Sometimes 27. equilateral .