Based on the information, BC = [tex]\frac{1}{2} DE[/tex] statement is true.
What is SAS Similarity Theorem?
If two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.
Given
AB = BD
AC = CE
BC ║ DE
From the figure we can say that
AB = [tex]\frac{1}{2}AD[/tex] and AC = [tex]\frac{1}{2} AE[/tex]
< BAC = < DAE
∴ Δ ABC = Δ ADE (SAS)
From the triangle similarity theorem
[tex]\frac{BC}{DE}=\frac{AB}{AD}=\frac{1}{2}[/tex]
∴ BC = [tex]\frac{1}{2} DE[/tex]
Hence, based on the information above, BC = [tex]\frac{1}{2} DE[/tex] statement is true.
Find out more information about SAS Similarity Theorem here
https://brainly.com/question/25882965
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