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10. a) Both pairs of opposite sides parallel
b) Both pairs of opposite sides congruent
c) Any pair of consecutive angles supplementary
d) Opposite angles are congruent
e) Diagonals bisect each other
f) One pair of sides are parallel and congruent
11. a) Corollary 42a - If a quadrilateral is a parallelogram, then opposite angles are congruent.
b) Theorem 43 - If a quadrilateral is a parallelogram, then its diagonals bisect each other.
c) Theorem 41 - If a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent.
d) Theorem 41
e) Theorem 42 - If a quadrilateral is a parallelogram, then any pair of consecutive angles is supplementary.
f) Definition of Parallelogram - a quadrilateral with both pairs of opposite sides parallel.
12. a) 18
b) 105
c) 12
d) 30
e) 115
f) 30
g) 12; 4
h) 120
i) 15
j) 16
k) 79
13. True
14. True
15. True
16. False, the quadrilateral could be a kite.
B
A
C
D
17. True
18. False, the quadrilateral could be an isosceles trapezoid.
D
19.
A
ABC ADC
B
AB || DC
C
Y
B (3,2)
A (0,0)
C (7,2)
D (5,0)
The figure is not a parallelogram. No sides are congruent.
8
Unit V– Other Polygons