Problem 6a
- Angle DCB is supplementary to angle ADC and angle ABC. Reason: Adjacent angles in a parallelogram are always supplementary.
- AE = EC. Reason: The diagonals of any parallelogram always bisect each other. In other words, the diagonals cut each other in half.
- DC = AB. Reason: Opposite sides of a parallelogram are congruent.
- angle DCB = angle DAB. Reason: Opposite angles of a parallelogram are congruent.
- CD = AB. Reason: segment DC is the same as segment CD. The order of the endpoints does not matter when it comes to listing a segment. Opposite sides of a parallelogram are congruent.
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Problem 6b
Answers:
angle L = 129
angle S = 51
angle C = 129
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Work Shown:
angle U = 51 (given)
angle S = angle U (Opposite angles of a parallelogram are congruent)
L+U = 180 (adjacent angles in parallelogram are supplementary)
L = 180-U
angle L = 180-51
angle L = 129
angle C = angle L (Opposite angles of a parallelogram are congruent)
angle C = 129
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Problem 6c
Answers:
x = 33/4 = 8.25
y = 50
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Work Shown:
TI across the top is 4x+9
NA across the bottom is 42
TI = NA since opposite sides of a parallelogram are congruent
4x+9 = 42
4x = 42-9
4x = 33
x = 33/4
x = 8.25
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angle TAN = 3y
angle TIN = 150
angle TAN = angle TIN (opposite angles of parallelogram are congruent)
3y = 150
y = 150/3
y = 50
