Question

The triangles are similar by:

the ASA similarity theorem.
the SSS similarity theorem.
the AAS similarity theorem.
the AA similarity postulate.
the SAS similarity theorem.

Answer 1

E. by the SAS similarity theorem.

Explanation:

Included angle x° in ∆ ABC ≅ included angle x° in ∆EDC (vertical angles are equal)

DC/BC = 240/150 = 1.6

EC/AC = 320/200 = 1.6

This implies that the ratio of two corresponding sides of both triangles are the same.

Two triangles are considered similar to each other by the SAS similarity theorem of they have a corresponding included angle that is equal and two corresponding sides that are congruent to each other. Therefore, both triangles are similar by the SAS similarity theorem.