Download Copyright © by Holt, Rinehart and Winston

Name _______________________________________ Date ___________________ Class __________________
Practice A
Conditions for Parallelograms
For each definition or theorem, tell what information you would
need about the figure to conclude that the figure is a parallelogram.
For some exercises, there is more than one correct answer, but give
only one example per exercise.
1. If both pairs of opposite angles of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
_____________________________
2. If both pairs of opposite sides of a quadrilateral are
parallel, then the quadrilateral is a parallelogram.
_____________________________
3. If an angle of a quadrilateral is supplementary to both of its
consecutive angles, then the quadrilateral is a parallelogram.
________________________________________________________________________________________
4. If one pair of opposite sides of a quadrilateral are parallel and congruent,
then the quadrilateral is a parallelogram.
________________________________________________________________________________________
5. If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a
parallelogram. (Hint: The diagonals of the figure are WY and XZ. )
________________________________________________________________________________________
6. If both pairs of opposite sides of a quadrilateral are
congruent, then the quadrilateral is a parallelogram.
_____________________________
A quadrilateral has vertices E(1, 1), F(4, 5), G(6, 6), H(3, 2).
Complete Exercises 7–10 to tell whether EFGH is a parallelogram.
7. Plot the vertices and draw EFGH.
8. Use the Distance Formula: EF  ________ HG  ________
9. Use the Slope Formula: slope of EF  ________
slope of HG  ________
10. The answers to Exercises 8 and 9 prove that EFGH is a
parallelogram. Which one of Exercises 1–6 states the
theorem that you used? ________
This desk lamp has a circular base and a movable arm in the shape
of a parallelogram. Use the figure to answer Exercises 11–13.
11. AD is vertical. Name another side of parallelogram ABCD that is
also vertical. ________
12. Because AD is attached to the base, AD stays vertical as the arm is
moved. Tell what happens to BC as the arm is moved up or down.
________________________________________________________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry
Name _______________________________________ Date ___________________ Class __________________
2.Possible answer: Use the slope formula to
find the slope of each side: slope of
b
b
, slope of GH 
, slope
EF 
ac
ac
b
b
of FG 
, slope of EH 
.
ac
ac
Segments with equal slopes are
parallel, so EF is parallel to GH and
FG is parallel to EH. Therefore EFGH
is a parallelogram.
3. 80 books
4. 92 books
5. 9    15
6. x    3x
7. 0    2x
Reteach
1. 10 cm
 3. 12 m
5. 62
7. 32
9. 36
11. 48
13. D(0, 3)
Challenge
2. 70
4. 10 m
6. 18 m
8. 9 m
10. 36
12. 132
14. N(2, 4)
2. m7
3. 90°
4. m5
5. 180°
6. 180°
8. mDAB
10. supplementary
11. supplementary
12. Converse of the Same-Side Interior
Angles 13. definition
14. Yes; explanations will vary.
15. No; the puck will have to land in the
goal.
16. No; explanations will vary.
Problem Solving
1. mC  135; mD  45
 2. 15 in.
4. 65
6. H
3. 4.5 ft
5. B
7. D
Reading Strategies
1. 100 mm
4. 42
 5. 138
6. 12 in.
7. 18 in.
8. 12 in.
9. 24 in.
10. 36 in.
CONDITIONS FOR
PARALLELOGRAMS
Practice A
1. W  Y and X  Z
2. WX ZY and WZ XY
3. Possible answer: W is supplementary
to X and to Z.
4. Possible answer: WX ZY and
1. Triangle Sum
7. mCDA
9. 360°
 3. 86 mm
WX  ZY
5. WY and XZ bisect each other.
6. WX  ZY and WZ  XY
7.
8. 5; 5
10. 4
9.
4 4
;
3 3
11. BC
12. BC moves up or down but stays
vertical.
Practice B
1. ABCD is a parallelogram. mA  mC
 72 and mB  mD  108
  EFGH is not a parallelogram. HI  8.6
and FI  7.6. EG does not bisect HF .
3. No, the diagonals do not necessarily
bisect each other.
4. Yes, the triangles with numbered angles
are  by AAS. By CPCTC, the parallel sides
are congruent.
2. 138
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
Holt McDougal Geometry