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: mA = ______mD = ______mB = ______mE = ______mC = ______mF = ______

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 m2  25 and m9  48 , then mSPQ = _____

7. If PQ = 7x – 3 and SR = 5x + 5, then PQ = ______

2 8. If ST = 8, then SQ = _____

9. If mPSR  75 , then mPQR = _____, mQRS = ______

RSTU is a rectangle. Find the unknown measure(s).

10. If m1  9x  3 and m3  7x  5, then m3 = ______

11. If RV = 4x + 1 and RT = 10x – 2 , then RT = ______

12. If m11 11x  4 and m7  6x 1, then m7 = ______

13. If m4  54 , then m5= ______and m2 = ______

JKLM is a rhombus. Find the unknown measure(s).

14. If MN = 6x – 5 and NK = 4x + 1, then MK = ______

15. If m10  7x 8, then x = ______

16. If m6  52 , then mJKL = _____

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 m3  8x  2 , then x = ______

20. If AE = 19, then DB = ______

21. m1 = ______

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 m6  43 , then m4 = _____, m5 = _____ and m2 = _____

4 ABCD is a kite. Find the unknown measure.

26. If AB = 8x – 2, and AD = 6x + 4, then AD = ______

27. If mCED  7x  6, then x = _____

28. If mABC 12x 10 and mADC 15x 14 , then mADC = ______

29. If mBAC  24 , then mDAC = ______

5 Answers to Chapter 6 Review -

1. 900˚ 2. Int: 172˚ Ext: 8˚ 3. 6 4. x = 18, mA = 108˚, mB = 126˚ mC = 90˚, mD = 144˚, mE= 144˚, mF = 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