Question

I dont understand can someone help

Answer 1

9514 1404 393

Answer:

• FE = 10
• FL = 4.8

Explanation:

The given parallel lines mean that the two triangles are similar:

∆FDE ~ ∆FLK

That means corresponding sides are proportional.

FE/FK = ED/KL

FE = FK(ED/KL) = 4(15/6) = 10

and

FL/FD = KL/ED

FL = FD·KL/ED = 12(6/15) = 12(2/5) = 4.8

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Additional comment

Each of the diagonal lines, LD and KE, can be considered to be transversals between the parallel lines DE and KL. This means the interior angles at either end of those diagonals will be congruent. Hence the triangles are similar by the AA postulate.