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Moderate

Congruent Triangles: Isosceles and Equilateral

ACTMAT-KTFKSG

In the figure below, $ {\Delta}ADE $ is isosceles with $ \overline{AE} = \overline{DE} $, and $ {\Delta}BCE $ is equilateral.

Which of the following statements is/are true?

I. $ {\Delta ABE ~ \Delta DCE} $

​II. $ {\Delta ABE \cong \Delta DCE} $

III. $ {\Delta ACE \cong \Delta DBE} $

A

$\text{I only}$

B

$\text{III only}$

C

$\text{I and II only}$

D

$\text{I and III only}$

E

$\text{I, II, and III}$