Given: AB II DC and mZ2 = m24
Prove: AD | BC
Reasons
given
Statements
1. AB DC
2. m 22=m24
3. 21 and 24 are supplements
5. mZ1+mZ2= 180°
6. 21 and 2 are supplements
7. AD BC
2. given
3. same side interior angles thm
4. def. of supplementary angles
5. substitution
6. def. of supplementary angles
converse same side interior angles thm.

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.