Answer:
Step-by-step explanation:
Statement Reason
ΔACE, BD║AE Given
∠4≅∠1 and ∠3≅∠2 Corresponding angle postulate
ΔACE is similar to ΔBCD Angle-Angle similarity postulate
[tex]\frac{CA}{CB}=\frac{CE}{CD}[/tex] Definition of similar triangles
CA=CB+BA and CE=CD+DE Segment addition postulate
[tex]\frac{CB+BA}{CB}=\frac{CD+DE}{CD}[/tex] Substitution property of equality.
[tex]\frac{CB}{CB}+\frac{BA}{CB}=\frac{CD}{CD}+\frac{DE}{CD}[/tex] Addition of fractions.
[tex]1+\frac{BA}{CB}=1+\frac{DE}{CD}[/tex] Simplification of fractions
[tex]\frac{BA}{CB}=\frac{DE}{CD}[/tex] Subtraction property of equality.
