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Name: __________________________________________ Period: ___________ Geometry Honors Unit 6: Quadrilaterals Homework Section 6.1: Classifying Quadrilaterals State whether each statement is true or false. Justify your response. 1. All squares are rectangles. 2. A rhombus can be a kite. 3. Every quadrilateral is a parallelogram. 4. A trapezoid is a parallelogram. 5. Some parallelograms are squares. 6. All rhombuses are squares. Name each type of special quadrilateral that can meet the given condition. Make sketches to support your answers. 7. Exactly one pair of congruent sides 8. Four right angles 9. Two pairs of parallel sides 10. Adjacent sides that are congruent State all possible names for each figure and then circle the most precise name for each figure. 11. 12. 13. 14. 15. 16. 17. 18. Find the value of the variables. Then find the lengths of the sides of each quadrilateral. 19. 20. 21. Find the measure of the variable and each angle. 22. 23. 24. 25.
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Sep 03, 2018

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Page 1: Name:& &&Period:& & Geometry&Honors& - Manatee … · 2013-04-29 · ... &_____& Geometry&Honors& Unit&6:&Quadrilaterals& & Homework& & Section(6.1:(Classifying(Quadrilaterals(Statewhether&each&statement&is&trueor&false.&Justify

Name:  __________________________________________    Period:  ___________   Geometry  Honors  Unit  6:  Quadrilaterals     Homework    

Section  6.1:  Classifying  Quadrilaterals  State  whether  each  statement  is  true  or  false.  Justify  your  response.  

1. All  squares  are  rectangles.  2. A  rhombus  can  be  a  kite.  3. Every  quadrilateral  is  a  parallelogram.  

4. A  trapezoid  is  a  parallelogram.  5. Some  parallelograms  are  squares.  6. All  rhombuses  are  squares.  

 Name  each  type  of  special  quadrilateral  that  can  meet  the  given  condition.  Make  sketches  to  support  your  answers.  

7. Exactly  one  pair  of  congruent  sides  8. Four  right  angles  

9. Two  pairs  of  parallel  sides  10. Adjacent  sides  that  are  congruent  

 State  all  possible  names  for  each  figure  and  then  circle  the  most  precise  name  for  each  figure.  

11.  

12.  

13.  

14.  

15.  

16.  

17.  

18.  Find  the  value  of  the  variables.  Then  find  the  lengths  of  the  sides  of  each  quadrilateral.  

19.   20.   21.  Find  the  measure  of  the  variable  and  each  angle.  

22.  

23.  

24.  

25.

       

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Section  6.2:  Properties  of  Parallelograms  Find  the  value  of  x  in  each  parallelogram.  

1.  

2.  

3.  

4.  

5.  

6.  

7.  

8.  

 Find  the  measures  of  the  numbered  angles  for  each  parallelogram.  

9.  

10.  

11.  

12.  

13.  

14.  

15.  

16.    

 Find  the  length  of  𝑇𝐼  in  each  parallelogram.  

17.  18.   19.  

20.

   If  AE=17  and  BF=18,  find  the  measures  of  the  sides  of  parallelogram  BNXL.  

21. BN  22. NX  23. XL  24. BL  

                   

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Section  6.3:  Proofs  involving  Parallelograms  State  whether  the  information  given  about  quadrilateral  SMTP  is  sufficient  to  prove  that  it  is  a  parallelogram.  

1. ∠SPT  ≅  ∠SMT  2. ∠SPX  ≅  ∠TMX,  ∠TPX  ≅  ∠SMX  3. 𝑆𝑀 ≅ 𝑃𝑇, 𝑆𝑃 ≅ 𝑀𝑇  

4. 𝑆𝑋 ≅ 𝑋𝑇, 𝑆𝑀 ≅ 𝑃𝑇  5. 𝑃𝑋 ≅ 𝑀𝑋, 𝑆𝑋 ≅ 𝑇𝑋  6. 𝑆𝑃 ≅ 𝑀𝑇, 𝑆𝑃 ∥ 𝑀𝑇  

Find  the  values  of  x  and  y  for  which  the  figure  must  be  a  parallelogram.  

7.   8.   9. Find  the  value  of  x.  Then  tell  whether  the  figure  must  be  a  parallelogram.  Explain  your  answer.  

10.   11.  12.

Decide  whether  the  quadrilateral  is  a  parallelogram.  Explain  your  answer.  

13.  

14.  

15.  

16.  

17.  

18.  

19.  

20.  Section  6.4:  Special  Parallelograms  (rhombuses,  rectangles,  and  squares)  For  each  parallelogram  choose  the  best  name  and  find  the  measures  of  the  numbered  angles.  

1.  

2.  

3.  

4.  

5.  

6.

HIJK  is  a  rectangle.  Find  the  value  of  x  and  the  length  of  each  diagonal.  7. HJ  =  x  and  IK  =  2x  –  7  8. HJ  =  3x  +  5  and  IK  =  5x  –  9  

9. HJ  =  3x  +  7  and  IK  =  6x  –  11  10. HJ  =  19  +  2x  and  IK  =  3x  +  22  

 

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The  parallelograms  below  are  not  drawn  to  scale.  Can  the  parallelogram  have  the  conditions  marked?  If  not,  write  impossible.  Explain  your  answer.    

11.  

12.  

13. For  each  rhombus  find  the  measures  of  the  numbered  angles.  

14.  

15.  

16.

Determine  whether  the  quadrilateral  can  be  a  parallelogram.  If  not,  write  impossible.  Explain  your  answer.  17. One  pair  of  opposite  sides  is  parallel  and  the  other  pair  is  congruent.  18. Opposite  angles  are  congruent  and  supplementary,  but  the  quadrilateral  is  not  a  rectangle.  

Do  the  following  properties  apply  to  rectangles,  rhombi,  and/or  squares?  List  all  that  apply.  19. All  sides  are  congruent.  20. Opposite  sides  are  congruent.  21. Opposite  sides  are  parallel.  22. Opposite  angles  are  congruent.  23. All  angles  are  right.  

24. Consecutive  angles  are  supplementary.  25. Diagonals  bisect  each  other.  26. Diagonals  are  congruent.  27. Diagonals  are  perpendicular.  28. Each  diagonal  bisects  opposite  angles.  

 Section  6.5:  Trapezoids  and  Kites  Find  the  measures  of  the  numbered  angles  in  each  isosceles  trapezoid.  

1.  

2.  

3.  

4.  

5.  

6.  

Find  the  value  of  the  variable(s)  in  each  isosceles  trapezoid.  

7.  

8.  

9.  

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Find  the  measures  of  the  numbered  angles  in  each  kite.  

10.  

11.  

12.  

13.  

14.  

15. Find  the  value  of  the  variable(s)  in  each  kite.  

16.   17.   18. Can  two  angles  of  a  kite  be  as  follows?  Explain.  

19. Opposite  and  acute  20. Consecutive  and  obtuse  21. Opposite  and  supplementary  

22. Consecutive  and  supplementary  23. Opposite  and  complementary  24. Consecutive  and  complementary  

 Unit  6  Review  Find  the  correct  word  that  completes  each  sentence.  

1. A(n)  ______________________  is  a  parallelogram  with  four  right  angles.  2. A(n)  ______________________  is  a  quadrilateral  with  two  pairs  of  adjacent  sides  congruent  and  no  opposite  

sides  congruent.  3. Angles  of  a  polygon  that  share  a  common  side  are  ______________________.  4. A(n)  ______________________  is  a  quadrilateral  with  exactly  one  pair  of  parallel  sides.  5. A(n)  ______________________  is  a  parallelogram  with  four  congruent  sides.  6. The  ______________________  of  a  trapezoid  is  the  segment  that  joins  the  midpoints  of  the  nonparallel  

opposite  sides.  7. A(n)  ______________________  is  a  quadrilateral  with  both  pairs  of  opposite  sides  parallel.  8. A(n)  ______________________  is  a  parallelogram  with  four  congruent  sides  and  four  right  angles.  9. A(n)  ______________________  is  a  trapezoid  whose  nonparallel  opposite  sides  are  congruent.  10. Two  angles  that  share  a  base  of  a  trapezoid  are  its  ______________________.  

Find  the  values  of  the  variables  and  the  lengths  of  the  sides.  

11.   12.      

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Find  the  measures  of  the  numbered  angles  for  each  parallelogram.  

13.  

14.   15.

Determine  whether  the  quadrilateral  must  be  a  parallelogram.  

16.   17.   18.   19. Find  the  values  of  the  variables  for  which  ABCD  must  be  a  parallelogram.  

20.  

21.  

22.  

23. Find  the  measures  of  the  numbered  angles  in  each  quadrilateral.  

24.   25.   26.  27.

Find  AC  for  each  quadrilateral.  

28.  29.  

30.

Does  the  information  allow  you  to  prove  that  ABCD  is  a  parallelogram?  Explain.    31. 𝐴𝐶  bisects  𝐵𝐷  32. 𝐴𝐵 ≅ 𝐷𝐶,𝐴𝐵 ∥ 𝐷𝐶  

33. ∠DAB≅∠BCD  and  ∠ABC≅∠CDA  34. 𝐴𝐵 ≅ 𝐷𝐶,𝐵𝐶 ≅ 𝐴𝐷  

Find  the  values  of  x  and  y  in  parallelogram  ABCD.  35. AB  =  2y,  BC  =  y  +  3,  CD  =  5x  –  1,  DA  =  2x  +  4   36. AB  =  2y  +  1,  BC  =  y  +  1,  CD  =  7x  –  3,  DA  =  3x  

Determine  whether  each  statement  is  always,  sometimes  or  never  true.  37. A  rhombus  is  a  square.  38. A  square  is  a  rectangle.  39. A  rhombus  is  a  rectangle.  

40. The  diagonals  of  a  parallelogram  are  perpendicular.  41. The  diagonals  of  a  parallelogram  are  congruent.  42. Opposite  angles  of  a  parallelogram  are  congruent.