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
