Explain why the triangle are similar and write a similarity statement.

a.$\mathrm{\angle}A\stackrel{\sim}{=}\mathrm{\angle}BED\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\mathrm{\angle}C\stackrel{\sim}{=}\mathrm{\angle}BDE$ by the Alternate Interior Angles Theorem.

$\mathrm{\u25b3}ABC\sim \mathrm{\u25b3}EBD$ by AA Similarity.

b.$\mathrm{\angle}A\stackrel{\sim}{=}\mathrm{\angle}BDE\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\mathrm{\angle}C\stackrel{\sim}{=}\mathrm{\angle}BED$ by the Corresponding Angles Postulate.

$\mathrm{\u25b3}ABC\sim \mathrm{\angle}DBE$ by AA Similarity.

c.$\mathrm{\angle}A\stackrel{\sim}{=}\mathrm{\angle}BDE\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\mathrm{\angle}C\stackrel{\sim}{=}\mathrm{\angle}BED$ by the Corresponding Angles Postulate.

$\mathrm{\u25b3}ABC\sim \mathrm{\u25b3}EBD$ by AA Similarity.

d.$\mathrm{\angle}A\stackrel{\sim}{=}\mathrm{\angle}BDE\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}\mathrm{\angle}C\stackrel{\sim}{=}\mathrm{\angle}BED$ by the Alternate Interior Angles Theorem.

$\mathrm{\u25b3}ABC\sim \mathrm{\u25b3}DBE$ by AA Similarity.

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