· web viewname: _period: _ ch 5-6 review worksheet determine the coordinates of each...

Name: _______________________________________________ Period: __________________Ch 5-6 Review Worksheet

Determine the coordinates of each translated image without graphing.

1.The vertices of parallelogram HJKL are , , , and . Translate the parallelogram 7 units up to form parallelogram .

2.The vertices of quadrilateral WXYZ are , and Z (3, 7). Translate the quadrilateral 5 units to the right and 8 units down to form quadrilateral .

Determine the coordinates of each rotated image without graphing.

3.The vertices of triangle RST are R (0, 3), S (2, 7), and . Rotate the triangle about the origin counterclockwise to form triangle .

4.The vertices of quadrilateral WXYZ are , and Z (3, 7). Rotate the quadrilateral about the origin counterclockwise to form quadrilateral .

Determine the coordinates of each reflected image without graphing.

5.The vertices of triangle RST are R (0, 3), S (2, 7), and . Reflect the triangle over the x-axis to form triangle .

6.The vertices of quadrilateral WXYZ are , and Z (3, 7). Reflect the quadrilateral over the y-axis to form quadrilateral .

7. Identify the transformation used to create on each coordinate plane. Identify the congruent angles and the congruent sides. Then, write a triangle congruence statement.

7.

List the corresponding sides and angles, using congruence symbols, for each pair of triangles represented by the given congruence statement.

8.

9.

Determine whether each pair of given triangles are congruent. Use the Distance Formula and a protractor when necessary.

10. Congruent by SSS? 11. Congruent by SAS?

Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent by SAS.

12. In , and . In , and .


14.

15.

Determine whether there is enough information to prove that each pair of triangles are congruent by SSS or SAS. Write the congruence statements to justify your reasoning.

16. 17.

18. 19.

20. 21.

22. 23.

Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent by ASA.



30. Determine whether is congruent to by ASA.

31. Determine whether is congruent to by AAS.

32. Determine whether is congruent to by AAS.

Determine the angle measure or side measure that is needed in order to prove that each set of triangles are congruent by AAS.



35. 36.

Determine whether there is enough information to prove that each pair of triangles are congruent by ASA or AAS. Write the congruence statements to justify your reasoning.

39. 40.

41. 42.

43. 44.

45. 46.

Mark the appropriate sides to make each congruence statement true by the Hypotenuse-Leg Congruence Theorem.

47. 48.

Mark the appropriate sides to make each congruence statement true by the Leg-Leg Congruence Theorem.49. 50.

Mark the appropriate sides and angles to make each congruence statement true by the Hypotenuse-Angle Congruence Theorem.

51. 52.

Mark the appropriate sides and angles to make each congruence statement true by the Leg-Angle Congruence Theorem.

53. 54.

Create a two-column proof to prove each statement.

55. Given:

Prove:

56. Samantha is hiking through the forest and she comes upon a canyon. She wants to know how wide the canyon is. She measures the distance between points A and B to be 35 feet. Then, she measures the distance between points B and C to be 35 feet. Finally, she measures the distance between points C and D to be 80 feet. How wide is the canyon? Explain.

57. Explain why . 58. Calculate MR given that the perimeter of is 60 centimeters.

Determine the value of x in each isosceles triangle.

59. 60.

63. 64.

65. A kaleidoscope is a cylinder with mirrors inside and an assortment of loose colored beads. When a person looks through the kaleidoscope, different colored shapes and patterns are created as the kaleidoscope is rotated. Suppose that the diagram represents the shapes that a person sees when they look into the kaleidoscope. Triangle AEI is an isosceles triangle with bisects and bisects . What is the length of , if one half the length of is 14 centimeters? Explain.

Write the converse of each conditional statement. Then, determine whether the converse is true.

66. If the lengths of the sides of a triangle are 3 cm, 4 cm, and 5 cm, then the triangle is a right triangle.

67. If the corresponding sides of two triangles are congruent, then the triangles are congruent.

68. If the corresponding angles of two triangles are congruent, then the triangles are similar.

Write the inverse of each conditional statement. Then, determine whether the inverse is true.69. If two angles are complementary, then the sum of their measures is .

70. If a polygon is a square, then it is a rhombus.

71. If a polygon is a trapezoid, then it is a quadrilateral.

Write the contrapositive of each conditional statement. Then, determine whether the contrapositive is true.72. If two angles are supplementary, then the sum of their measures is .

73. If the radius of a circle is 8 meters, then the diameter of the circle is 16 meters.

74. If the diameter of a circle is 12 inches, then the radius of the circle is 6 inches.

For each pair of triangles, use the Hinge Theorem or its converse to write a conclusion using an inequality,

75.

76.

ch 5-6 review worksheetAnswer Section

1. ANS:The vertices of parallelogram are , , , and .

PTS: 1 REF: 5.1 NAT: G.CO.2 | G.CO.3 | G.CO.5TOP: Skills Practice

2. ANS:The vertices of quadrilateral are , , , and .


3. ANS:The vertices of triangle are , and .


4. ANS:The vertices of quadrilateral are , and .


5. ANS:The vertices of triangle are , and .


6. ANS:The vertices of quadrilateral are , and .


7. ANS:Triangle BND was translated 10 units to the right to create triangle XYZ.


8. ANS:


9. ANS:


10. ANS:

The triangles are not congruent.

PTS: 1 REF: 5.3 NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12TOP: Skills Practice KEY: Side-Side-Side Congruence Theorem

11. ANS:

The triangles are congruent by the SAS Congruence Theorem.

PTS: 1 REF: 5.4 NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12TOP: Skills Practice KEY: Side-Angle-Side Congruent Theorem

12. ANS:


13. ANS:


14. ANS:


15. ANS:


16. ANS:The triangles are congruent by SSS.


17. ANS:There is not enough information to determine whether the triangles are congruent by SSS or SAS. SAS does not apply because the congruent angles in the figure are not included angles.


18. ANS:The triangles are congruent by SAS.


19. ANS:There is not enough information to determine whether the triangles are congruent by SSS or SAS. SAS does not apply because the congruent angles in the figure are not included angles.

PTS: 1 REF: 5.4 NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12

TOP: Skills Practice KEY: Side-Angle-Side Congruent Theorem20. ANS:

The triangles are congruent by SAS.


21. ANS:There is not enough information to determine whether the triangles are congruent by SSS or SAS.


22. ANS:The triangles are congruent by SAS.


23. ANS:The triangles are congruent by SSS.


30. ANS:

The triangles are congruent by the ASA Congruence Theorem.

PTS: 1 REF: 5.5 NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12TOP: Skills Practice KEY: Angle-Side-Angle Congruence Theorem

24. ANS:


25. ANS:


26. ANS:


27. ANS:


28. ANS:


29. ANS:


31. ANS:

The triangles are not congruent.

PTS: 1 REF: 5.6 NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12TOP: Skills Practice KEY: Angle-Angle-Side Congruence Theorem

32. ANS:

The triangles are congruent by the AAS Congruence Theorem.


33. ANS:


34. ANS:


35. ANS:


36. ANS:


37. ANS:


38. ANS:


39. ANS:The triangles are congruent by AAS.


40. ANS:There is not enough information to determine whether the triangles are congruent by ASA or AAS.


41. ANS:The triangles are congruent by ASA.




43. ANS:There is not enough information to determine whether the triangles are congruent by ASA or AAS.








47. ANS:

PTS: 1 REF: 6.1 NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 | G.MG.1TOP: Skills PracticeKEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | Hypotenuse-Angle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem

48. ANS:


49. ANS:


50. ANS:


51. ANS:


52. ANS:


53. ANS:

PTS: 1 REF: 6.1 NAT: G.CO.6 | G.CO.7 | G.CO.8 | G.CO.10 | G.CO.12 | G.MG.1TOP: Skills Practice

KEY: Hypotenuse-Leg (HL) Congruence Theorem | Leg-Leg (LL) Congruence Theorem | Hypotenuse-Angle (HA) Congruence Theorem | Leg-Angle (LA) Congruence Theorem

54. ANS:


55. ANS:

Statements Reasons

1. 1. Given

2. 2. Base Angle Converse Theorem

3. 3. Given

4. 4. Given

5. 5. SSS Congruence Theorem

6. 6. CPCTC

PTS: 1 REF: 6.2 NAT: G.CO.10 | G.MG.1TOP: Skills PracticeKEY: corresponding parts of congruent triangles are congruent (CPCTC) | Isosceles Triangle Base Angle Theorem | Isosceles Triangle Base Angle Converse Theorem

56. ANS:The canyon is 80 feet wide.

The triangles are congruent by the Leg-Angle Congruence Theorem. Corresponding parts of congruent triangles are congruent, so .


57. ANS:

Using and the Base Angle Theorem, . Using and the Base Angle Theorem, . Since and are supplementary, . Since the sum of the measures of the angles in a triangle is , .


58. ANS: cm. Using the Base Angle Converse Theorem, . Solve the perimeter equation

, where and . So, .


59. ANS:

PTS: 1 REF: 6.3 NAT: G.CO.10 | G.MG.1TOP: Skills PracticeKEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem | Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem

60. ANS:


61. ANS:


62. ANS:


63. ANS:

PTS: 1 REF: 6.3 NAT: G.CO.10 | G.MG.1TOP: Skills PracticeKEY: vertex angle | Isosceles Triangle Base Theorem | Isosceles Triangle Vertex Angle Theorem |

Isosceles Triangle Perpendicular Bisector Theorem | Isosceles Triangle Altitude to Congruent Sides Theorem | Isosceles Triangle Angle Bisector to Congruent Sides Theorem

64. ANS:


65. ANS:The length of is 28 centimeters.

By the Isosceles Triangle Angle Bisector to Congruent Sides Theorem, and are congruent. Since half the length of is 14 centimeters, its full length is 28 centimeters. Therefore, the length of is 28 centimeters. So, the length of is 28 centimeters.


66. ANS:The converse of the conditional would be:

If a triangle is a right triangle, then the lengths of its sides are 3 cm, 4 cm, and 5 cm.

The converse is not true.

PTS: 1 REF: 6.4 NAT: G.CO.10 | G.MG.1TOP: Skills PracticeKEY: inverse | contrapositive | direct proof | indirect proof or proof by contradiction | Hinge Theorem | Hinge Converse Theorem


If two triangles are congruent, then the corresponding sides of the two triangles are congruent.

The converse is true.



If two triangles are similar, then the corresponding angles of the two triangles are congruent.

The converse is true.


69. ANS:The inverse of the conditional would be:

If two angles are not complementary, then the sum of their measures is not .

The inverse is true.



If a polygon is not a square, then it is not a rhombus.

The inverse is not true.



If a polygon is not a trapezoid, then it is not a quadrilateral.

The inverse is not true.


72. ANS:The contrapositive of the conditional would be:

If the sum of the measures of two angles is not , then the angles are not supplementary.

The contrapositive is true.


73. ANS:

The contrapositive of the conditional would be:

If the diameter of a circle is not 16 meters, then the radius of the circle is not 8 meters.



74. ANS:The contrapositive of the conditional would be:

If the radius of a circle is not 6 inches, then the diameter of the circle is not 12 inches.



75. ANS:


76. ANS:


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