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