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LESSON
6-3
Practice C
Conditions for Parallelograms
1. In parallelogram ABCD, AC  3 13 and BD  5 5 . AC is contained in the line
11
3
with equation y  x  2, and BD is contained in the line with equation y  x  6.
2
2
If A and B are both in Quadrant I, find the vertices of ABCD.
(Hint: All coordinates are in integers.)
Use the figure for Exercises 2 and 3. A  B and C  D.
2. Name the conditions under which the figure would be a parallelogram.
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3. Tell which sides of the figure must be parallel under all conditions. Explain your answer.
4. Sketch a parallelogram with perpendicular diagonals. Tell which sides and angles
of the parallelogram have to be congruent. Explain your answer.
5. Sketch a parallelogram with perpendicular congruent diagonals. Tell which sides and
angles of the parallelogram have to be congruent. Explain your answer.
6. Find the measure(s) of the parallelogram’s angles in your sketch for Exercise 5.
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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
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Holt Geometry
Name _______________________________________ Date ___________________ Class __________________
parallelogram have measure 90°.
6. 90°
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