Prove that the segments joining the midpoint of consecutive sides of an isosceles trapezoid form a rhombus.
find the slope of de and fg.

See explanation

Step-by-step explanation:

a) To prove that DEFG is a rhombus, it is sufficient to prove that:

Using the distance formula;

Using the slope formula;

The slope of EG is

The slope of EG is undefined hence it is a vertical line.

The slope of  DF is

The slope of DF is zero, hence it is a horizontal line.

A horizontal line meets a vertical line at 90 degrees.

Conclusion:

Since and , DEFG is a rhombus

b) Using the slope formula:

The slope of DE is

The slope of FG is

the answer is vanilla

step-by-step explanation:

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18