Download Copyright © by Holt, Rinehart and Winston

Name ________________________________________ Date ___________________ Class __________________
LESSON
6-3
Practice A
Conditions for Parallelograms
For each statement, tell what information you would
need to show about the figure to conclude that the figure is a parallelogram.
R
List objects used with ,║, or 
connecting them:
Name of Formula
Needed:
Numbers
Should Be:
If both pairs of opposite sides of a
1. quadrilateral are parallel, then the
1.quadrilateral is a parallelogram.
1st pair of opposite sides:
>
>
2nd pair of opposite sides:
>
>
If oIf If one pair of opposite sides of a
2. quadrilateral are parallel and
congruent, then the quadrilateral
is a parallelogram.
Pair of opposite sides:
>
>
>
>
If the diagonals of a quadrilateral
3. bisect each other, then the
quadrilateral is a parallelogram.
Halves of 1st diagonal:
>
>
Halves of 2nd diagonal:
>
>
1st pair of opposite sides:
>
>
2nd pair of opposite sides:
>
>
Statement:
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.
5. Plot the vertices and draw EFGH.
6. Use the Distance Formula: EF  ________ HG  ________
7. Use the Slope Formula: slope of EF  ________
slope of HG  ________
8. The answers to Exercises 6 and 7 prove that EFGH is a
parallelogram. Which one of Exercises 1–4 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.
10. AD is vertical. Name another side of parallelogram ABCD that is
also vertical. ________
11. Because AD is attached to the base, AD stays vertical as the arm is
moved. Make a conjecture about 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.
A57
Holt Geometry
7. PQ  RS  26 ; QR  PS  5 2 ;
PQRS is a parallelogram.
LESSON 6-3
Practice A
8. Possible answer: UV  TW  2 5 ; slope of
UV  slope of TW  2; TUVW is a
parallelogram.
Practice C
1. W  Y and X  Z
2. WX ZY and WZ XY
3. Possible answer: W is supplementary
to X and to Z.
1. A(4, 4), B(2, 5), C(2, 5), D(0, 26)
2. Possible answer: A  C
4. Possible answer: WX ZY and
WX  ZY
3. AB || CD ; possible answer: because
A  B and C  D and the sum of
the interior angle measures of a
quadrilateral is 360°, 2mA  2mD 
360° or 2(mA  mD)  360°.
Therefore mA  mD  180°. A and
D are supplementary, so by the
Converse of the Same-Side Interior
Angles Theorem, AB || CD
5. WY and XZ bisect each other.
6. WX  ZY and WZ  XY
7.
8. 5; 5
10. 4
9.
4. All four sides are congruent, and the
two pairs of opposite angles are
congruent; possible answer: because
the diagonals are perpendicular, all four
angles created by the intersecting
diagonals are right angles and therefore
congruent. And because the diagonals
bisect each other, all four of the right
triangles are congruent by SAS. By
CPCTC, all four of the parallelogram’s
sides must be congruent. The two pairs
of opposite angles are congruent as for
any parallelogram.
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.
5.
4. Yes, the triangles with numbered angles
are  by AAS. By CPCTC, the parallel
sides are congruent.
5. No, x  x may not be 180.
6. slope of JK  slope of LM  1; slope
2

of KL  slope of JM  3 ; JKLM is a
parallelogram.
All four sides are congruent, and all
four angles are congruent; possible
answer: the sides are congruent for
the same reasons given in Exercise
4. But because the diagonals are
congruent and bisected, each right
triangle.created by the diagonals is
an isosceles right triangle. The acute
angles of these triangles have
measure 45°, so all the angles of the
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A57
Holt Geometry
Name _______________________________________ Date ___________________ Class __________________
parallelogram have measure 90°.
6. 90°
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
6-20
Holt Geometry