Geometry Diff Chapter 6 Test Review Answers pages 449 – 452 Problems 1 – 43 1. False, base Angles of an isosceles trapezoid are congruent. 2. True. 3. False, a diagonal is a segment that connects any two nonconsecutive vertices. 4. True. 5. True. 6. False, the midsegment of a trapezoid is the segment that connects the midpoints of the legs. 7. False, a rectangle is always a parallelogram. 8. False, a quadrilateral with only one set of parallel sides is a trapezoid. 9. True. 10. False, the leg of a trapezoid is one of the nonparallel sides. 11. sum =180 10− 2( ) =1440° 12. sum =180 15− 2( ) = 2340° 13. sum =180 6− 2( ) = 720° 14. exterior angle =180−135= 45° , then sides = 36045 = 8 15. exterior angle =180−166.15=13.85° , then sides = 360

13.85 = 26 16. m∠ADC =180−115= 65° 17. AD = BC = 18 18. AB = DC = 12 19. m∠BCD =m∠BAD =115°

20. 4x − 5= 2x + 92x =14x = 7

4y+83+ 42+ 23=1804y+148 =1804y = 32y = 8

21. 2x + 41=115

2x = 74x = 37

3y+13= 2y+19

y = 6

22. Need opposite sides parallel, or need opposite sides congruent or need opposite angles congruent

or need diagonals that bisect each other. 23. Yes, because the diagonals bisect each other. 24. Yes, because one set of opposite sides are both parallel and congruent. 25. Skip

26. 5x − 2 = 3x + 62x = 8x = 4

3y− 4 = y+122y =16y = 8

27. 3x − 6 = x + 42x =10x = 5

5y = 60y =12

28. 6x +12 = 5x + 20x = 8

, therefore the width = 5(8) + 20 = 60 inches.

29. m∠GEH = 90− 57 = 33° 30. m∠FGE = 90−13= 77° 31. EG = 2(32) = 64 32. m∠HEF +m∠EFG =180°

33. 4x − 6 = x +33x = 9x = 3

, therefore EF = 4(3) – 6 = 6

34. Because ΔAEB is a right triangle, then AE = 122 − 92 = 144−81 = 63 = 9 ⋅ 7 = 3 7 . 35. Because ΔDAB is isosceles, m∠BDA =m∠ABD = 55° . 36. CE = AE = 3 7 . 37. Because ΔBEC is a right triangle, m∠ACB = 90− 55= 35° . 38. FJ = FG = 2.5 cm

39. Using slopes:

Slope of QR = −6− 06−12

=−6−6

=1 Slope of ST = 6− 06− 0

=66=1

Slope of RS =0− −6( )0− 6

=6−6

= −1 Slope of QT = 6− 06−12

=6−6

= −1

This means opposite sides are parallel and consecutive sides are perpendicular.

Slope of QS = 0− 00−12

=0−12

= 0 Slope of RT =6− −6( )6− 6

=120= undefined

This means the diagonals are perpendicular. This shape is a Parallelogram, because opposite sides are parallel and a

Rectangle, because consecutive sides are perpendicular and Rhombus, because the diagonals are perpendicular and a Square, because it has properties of a rectangle and rhombus.

Using distances:

QR = 6−12( )2 + −6− 0( )2 = 36+36 = 72 ST = 6− 0( )2 + 6− 0( )2 = 36+36 = 72

SR = 0− 6( )2 + 0− −6( )( )2 = 36+36 = 72 QT = 6−12( )2 + 6− 0( )2 = 36+36 = 72

This means that all sides are congruent.

QS = 0−12( )2 + 0− 0( )2 = 144 =12 RT = 6− 6( )2 + 6− −6( )( )2 = 144 =12

This means the diagonals are congruent. This shape is a Parallelogram, because opposite sides are congruent and a

Rhombus, because all sides are congruent and a Rectangle, because diagonals are congruent and a Square, because it has the properties of a rhombus and rectangle.

40. Using slopes:

Slope of QR = 6− 45− −2( )

=27

Slope of ST = 2− 45−12

=−2−7

=27

Slope of RS = 4− 612− 5

=−27

Slope of QT = 2− 45− −2( )

=−27

This means opposite sides are parallel and consecutive sides are not perpendicular.

Slope of QS = 4− 412− −2( )

=014

= 0 Slope of RT = 2− 65− 5

=−40= undefined

This means the diagonals are perpendicular. This shape is a Parallelogram, because opposite sides are parallel and a

Rhombus, because the diagonals are perpendicular.

Using distances:

QR = 5− −2( )( )2 + 6− 4( )2 = 49+ 4 = 53 ST = 5−12( )2 + 2− 4( )2 = 49+ 4 = 53

SR = 12− 5( )2 + 4− 6( )2 = 49+ 4 = 53 QT = 5− −2( )( )2 + 2− 4( )2 = 49+ 4 = 53

This means that all sides are congruent.

QS = 12− −2( )( )2 + 4− 4( )2 = 196 =14 RT = 5− 5( )2 + 2− 6( )2 = 16 = 4

This means the diagonals are not congruent. This shape is a Parallelogram, because opposite sides are congruent and a

Rhombus, because all sides are congruent.

41. GH = 122 +152 = 144+ 225 = 369 = 9 ⋅ 41 = 3 41 42. m∠Z =180−112 = 68° 43a. The legs of the trapezoid must be congruent, or the diagonals of the trapezoid must be congruent. 43b. From the figure on the right, the length of each side of the large

square is 12 and the length of each side of the small square is 4. Then the diagonal of the small square is AC = 4 2 , the diagonal of the large square is EH =12 2 , therefore the length of each leg of the trapezoids is EA =GD = HC = FB = 1

2 12 2 − 4 2( ) = 12 8 2( ) = 4 2 . The

perimeter of each trapezoid is 12+ 4+ 4 2 + 4 2 =16+8 2 .