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Triangles ABC and DEF are shown below. Angle A measures 51°, angle Fmeasures
39°, and x = 6.
7.5
10
Is ABC is similar to DEF?

Triangles ABC and DEF are shown below Angle A measures 51 angle Fmeasures 39 and x 6 75 10 Is ABC is similar to DEF class=

Respuesta :

mlarsen5000

Answer:

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.

 ΔABC and ΔDEF are similar by AA Similarity Theorem.

   Given in the question,

In ΔABC,

  • m∠A = 51°
  • AB = 8 units
  • BC = 10 units

In ΔDEF,

  • m∠F = 39°
  • EF = 7.5 units

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]

Learn more,

brainly.com/question/3483803