Unit VI -- Geo1
1. AD = 21 Worksheet 6 (post pg.429,433)
2. HY = 7 3. ∠ITE = 70º ANSWER KEY
4. D
5. x = 2 or x = −6
if x = 2 then m∠B = 32 and m∠C = 148
if x = −6 then m∠B = 112 and m∠C = 68
6. 1. AFCE is a parallelogram
2. AE ≅ FC 1. given
2. opposite sides of a parallelogram are congruent
3. AF ≅ EC 4. AEC = AFC 5. BEC is supp to AEC 6. DFA is supp to AFC 7. BEC ≅ DFA 8. DAF ≅ BCE 9.  ADF ≅CBE 3. same as 2
4. opposite angles of a parallelogram are congruent
5. they form a linear pair
6. same as 4
7. supps of congruent angles are congruent
8. given
9. ASA (8, 3, 7)
10. AD ≅ BC 10.CPCTC
11. DF ≅ BE 11.CPCTC
12. AB ≅ DC 13.ABCD is a parallelogram
12.addition property (2, 11)
13.if both pairs of opposite sides of a quad are congruent,
then the quad is a parallelogram (10, 12)
7.
a. Always b. Sometimes (Yes: rectangle / No: plain parallelogram or rhombus)
c. Never d. Always
e. Sometimes (Yes: isos trap / No: rectangle)
f. Always g. Sometimes (Yes: square / No: plain rhombus)
h. Always i. Sometimes (Yes: isos / No: can have trap with two right angles that is not isos)
j. Sometimes (Yes: square / No: plain rhombus)
k. Sometimes (Yes: rhombus / No: plain parallelogram or a plain rectangle)
l. Sometimes (Yes: rectangle / No: kite) m. Always n. Always
o. Sometimes (Yes: square / No: plain rhombus)
p. Sometimes!!! (Yes: square. All squares are rhombuses so if it’s a square it’s a rhombus
No: Isos trap--there can be an isos trap with perpend diags... If the question had
been about parallelograms, the answer would have been always...)
q. Sometimes (Yes: square / No: isos trap)
8. mAB = −4
no pair of opposite sides are parallel ...
3
not a parallelogram or a trap
mBC = −5
AB = 10
no sides are congruent ...
5
not a kite!
mCD =
BC = 234
3
mAD = undefined
CD = 34
final answer:
quadrilateral
AD = 2
Worksheet 6 (post pg.429,433)
Unit VI -- Geo1
5
3
9. mAB = mBC = −
3
5
5
3
mCD = mAD = −
3
5
1
mAC = −4 mBD = 4
ANSWER KEY
both pairs of opposite sides parallel and
consecutive sides are perpendicular ...
at least a rectangle
diagonals are perpendicular ... final answer: square
10. mAB = 0 mBC = −3
mCD = 0 mAD = 3
one pair of opposite sides are parallel
and one pair of opposite sides are not
parallel ... at least a trapezoid
non-parallel sides of trap are congruent ... final answer: isos trap
AD = 40 BC = 40 2
3
2
mCD = 3 mAD =
3
11. mAB = 3 mBC =
both pairs of opposite sides parallel and
consecutive sides are not perpendicular ...
at least a parallelogram (not a rectangle)
consecutive sides of the parallelogram are not congruent,
so not a rhombus ... final answer: parallelogram
AB = 10 BC = 13 1
12. mAB = mBC = 2
2
1
mCD = mAD = 2
2
both pairs of opposite sides parallel and
consecutive sides are not perpendicular ...
at least a parallelogram (not a rectangle)
consecutive sides of the parallelogram are congruent ...
final answer: rhombus
AB = 20 BC = 20 3
4
−3
3
mCD = mAD =
4
4
13. mAB = undefined mBC =
AB = 7 DC = 3 2 14. quad
19. quad
24. quad
15. kite 20. square
25. quad
one pair of opposite sides are parallel
and one pair of opposite sides are not
parallel ... at least a trapezoid
non-parallel sides of the trap are not congruent, so not an isos trap
... final answer: trapezoid
16. rectangle 21. rhombus 26. square
17. rhombus 22. rectangle 27. square
18. rhombus
23. isos trap