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Triangle ADE is similar to triangle ABC. Which statement is TRUE concerning the slope of the line formed by the hypotenuse of each triangle? A) EA DE = CB AC B) DE EA = CB AC C) DE EA = AC CB D) EA DE = AC CB

Respuesta :

Answer:

[tex]B) \frac{DE }{EA} =\frac{CB}{AC}[/tex]

Step-by-step explanation:

If ant two given triangles are SIMILAR, then they have equal corresponding angles and their corresponding sides are PROPORTIONAL.

For example: if Δ ABC ≈ Δ PQR, then

∠A  = ∠P  , ∠B  = ∠Q  and ∠C  = ∠R

and [tex]\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}[/tex]

Now, here given:  Δ ADE ≈ Δ ABC

Then by the SIMILAR postulate their corresponding angles are equal and their corresponding sides are Proportional.

[tex]\implies \frac{AD}{AB} = \frac{DE}{BC} = \frac{AE}{AC}[/tex]    ............. (1)

Consider from above:

 [tex]\frac{DE}{BC} = \frac{AE}{AC}\\\implies \frac{DE}{AE} = \frac{BC}{AC}[/tex] ............. (2)

Here, the given options are:

[tex]A) \frac{EA }{DE} =\frac{CB}{AC}[/tex]     FALSE

[tex]B) \frac{DE }{EA} =\frac{CB}{AC}[/tex]   TRUE    (from 2)

[tex]C) \frac{DE }{EA} =\frac{AC}{CB}[/tex]   FALSE

[tex]C) \frac{EA}{DE} =\frac{AC}{CB}[/tex]    FALSE

notsally14

Answer:

b

Step-by-step explanation:

took test

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