Question

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

Answer 1

Answer:

$B) \frac{DE }{EA} =\frac{CB}{AC}$

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 $\frac{AB}{PQ} = \frac{BC}{QR} = \frac{AC}{PR}$

Now, here given:  Δ ADE ≈ Δ ABC

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

$\implies \frac{AD}{AB} = \frac{DE}{BC} = \frac{AE}{AC}$    ............. (1)

Consider from above:

 $\frac{DE}{BC} = \frac{AE}{AC}\\\implies \frac{DE}{AE} = \frac{BC}{AC}$ ............. (2)

Here, the given options are:

$A) \frac{EA }{DE} =\frac{CB}{AC}$     FALSE

$B) \frac{DE }{EA} =\frac{CB}{AC}$   TRUE    (from 2)

$C) \frac{DE }{EA} =\frac{AC}{CB}$   FALSE

$C) \frac{EA}{DE} =\frac{AC}{CB}$    FALSE