Write the following paragraph proof as a two-column proof.

Given:
A
⁢
B
=
C
⁢
D
and
B
⁢
C
=
D
⁢
E

Prove:
A
⁢
C
=
C
⁢
E



We're given that
A
⁢
B
=
C
⁢
D
. By the addition property of equality, we add
B
⁢
C
to both sides of the equation to get
A
⁢
B
+
B
⁢
C
=
C
⁢
D
+
B
⁢
C
. Since we're also given that
B
⁢
C
=
D
⁢
E
, we use the substitution property of equality to replace
B
⁢
C
with
D
⁢
E
on the right side of the equation. So,
A
⁢
B
+
B
⁢
C
=
C
⁢
D
+
D
⁢
E
. Next, by segment addition, we get that
A
⁢
B
+
B
⁢
C
is equal to
A
⁢
C
and that
C
⁢
D
+
D
⁢
E
is equal to
C
⁢
E
. Finally, we use the substitution property of equality on the equation
A
⁢
B
+
B
⁢
C
=
C
⁢
D
+
D
⁢
E
to replace
A
⁢
B
+
B
⁢
C
with
A
⁢
C
and
C
⁢
D
+
D
⁢
E
with
C
⁢
E
to get that
A
⁢
C
=
C
⁢
E
.

Type the correct answer in the box.