# Explain why the triangle are similar and write a similarity statement a \angle A\cong \angle BED\ and\ \angle C\cong \angle BDE

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

a. by the Alternate Interior Angles Theorem.
$\mathrm{△}ABC\sim \mathrm{△}EBD$ by AA Similarity.
b. by the Corresponding Angles Postulate.
$\mathrm{△}ABC\sim \mathrm{\angle }DBE$ by AA Similarity.
c. by the Corresponding Angles Postulate.
$\mathrm{△}ABC\sim \mathrm{△}EBD$ by AA Similarity.
d. by the Alternate Interior Angles Theorem.
$\mathrm{△}ABC\sim \mathrm{△}DBE$ by AA Similarity.
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Step 1
Given:
Two triangles are given.
Step 2
From the given figure:
$⇒\mathrm{\angle }A\stackrel{\sim }{=}\mathrm{\angle }BDE$ (Corresponding angles postulate)
$⇒\mathrm{\angle }C\stackrel{\sim }{=}\mathrm{\angle }BED$ (Corresponding angles postulate)
So,
$⇒\mathrm{△}ABC\sim \mathrm{△}DBE$ (AA similarity postulate)
Option b is correct.