Let a, b, and c represent positive real numbers. Given that quadrilateral ABCD has vertices at A(0,0), B(a,0), C(a+b,c), and D(b,c), explain why ABCD must be a parallelogram.
What will be an ideal response?
Because 
or 0 and 
or 0, we see that 
and that 
. Likewise, 
so that 
; also, 
so that 
.
or 0 and or 0, we see that and that . Likewise, so that ; also, so that .Then 
so that 
. With both pairs of opposite sides being parallel, ABCD
is a parallelogram.
Mathematics
You might also like to view...
Perform the indicated operation.
- 
A. 
B. 
C. 
D. 
Mathematics
Find the area of the rectangle or square.Length = 10 yd, width = 6 yd
A. 32 yd2 B. 120 yd2 C. 16 yd2 D. 60 yd2
Mathematics
Solve the equation.-9 - 9x = 54
A. 72 B. 3 C. 76 D. -7
Mathematics
Solve the problem.A bacterial culture has an initial population of 10,000. If its population declines to 6000 in 8 hours, what will it be at the end of 10 hours? Assume that the population decreases according to the exponential model.
A. 2000 B. 5281 C. 2641 D. 5061
Mathematics