Question

Instructions: Find the missing length indicated.
I

Answer 1

x = 12 units

Explanation:

In the picture attached,

Since, DE and BC are the parallel lines,AC and AB are the transverse.

Therefore, ∠AED ≅ ∠ABC [Alternate angles]

∠ADE ≅ ∠ACB [Alternate angles]

ΔADE ~ ΔACB [By AA postulate of similarity]

By the property of similarity,

If two triangles are similar then their corresponding sides will be proportional.

`\frac{\text{AB}}{\text{AE}}=\frac{\text{AC}}{\text{AD}}`

`((4+8))/(4)=((6+x))/(6)`

`3=1+(x)/(6)`

x = 12

Therefore, length of missing segment is 12 units.