Triangles ABC and DEF are shown below. Angle A measures 51°, angle Fmeasures 39°, and x = 6.
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Is ABC is similar to DEF?

 ΔABC and ΔDEF are similar by AA Similarity Theorem.

   Given in the question,

In ΔABC,

In ΔDEF,

To prove these right triangles similar, we can use AA-Similarity Theorem,

By applying triangle sum theorem in ΔDEF,

m∠D + m∠E + m∠F = 180°

m∠D + 90° + 39° = 180°

m∠D = 51°

Hence, ∠D ≅ ∠A and ∠E ≅ ∠B

       Therefore, ΔABC ~ ΔDEF [By AA Similarity Theorem]

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Yes

Step-by-step explanation:

yes

They both have interior angles of 90-51-39, which automatically makes them similar.  You could also see the dilation factor of .75 based on the 2 sides of a right angle to prove it.