Refer to the figure and match the theorem that supports the statement.
1. if chords are =, then arcs are =. if bc = de, then arc bc = arc de
2. if arcs are =, then chords are =. if ax is perpendicular to bc, then bx = xc
3. diameters perpendicular to chords bisect the chord if arc bc = arc de, then bc = de

Step-by-step explanation:

Refer to the figure and match the theorem that supports the statement.

1.If chords are =, then arcs are =.  

If BC = DE, then Arc BC = Arc DE  

2.If arcs are =, then chords are =.  

If Arc BC = Arc DE, then BC = DE  

3.Diameters perpendicular to chords bisect the chord  

If AX is perpendicular to BC, then BX = XC

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is