Consider parallel lines cut by a transversal. explain which theorems, definitions, or combinations of both can be used to prove that alternate exterior angles are congruent.

Corresponding angle theorem, vertical angle theorem, and the transitive property of congruence.

Step-by-step explanation:

Considering a set of parallel lines cut by a transversal. (Refer the attached image).

Now that lines J and K are parallel, then by "corresponding angle theorem"

By "vertical angle theorem"

Using, "transitive property of congruence"

And that is our required proof. In this whole proof we have used "corresponding angle theorem", "vertical angle theorem", and the "transitive property of congruence".

step-by-step explanation:

d

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