Answer:
1. x = 5
Step-by-step explanation:
1.
The Trapezoid Midsegment Theorem states that a line segment connecting the midpoints of the legs of the trapezoid is parallel to the bases, and equal to half their sum.
In this problem you can see that 5x - 1 is the midsegment of the trapezoid, so using the rule:
[tex](21 + 27) / 2 = 5x -1[/tex]
solve:
[tex]48/2 = 5x-1\\24 = 5x - 1\\25 = 5x\\x= 5[/tex]
2. Diagonals are congruent
You can see in this picture that the diagonals are not always congruent:
