Question

Find segment DF. Picture will help you.

Answer 1

Therefore the Segment DF is 7.2 unit.

Explanation:

Given:

∠ABD ≅ ∠D

∠DCE ≅ ∠E

AC = 10

CE = 6

BD = 12

To Find:

DF = ?

Solution:

∠ABD ≅ ∠D .....Given

Which are Alternate Angles

AB || CD ..........Alternate Angles Theorem

∠DCE ≅ ∠E ....Given

Which are Corresponding Angles

CD || EF ............Corresponding Angles Theorem

Now we have,

If three or more parallel lines are cut by two transversals, then they divide the transversals proportionally.

AB || CD || EF cut by transversal BF and AE then

`(BD)/(DF)=(AC)/(CE)`

Substituting the values we get

`(12)/(DF)=(10)/(6)\\\\DE=(72)/(10)=7.2\ unit\\\\DF = 7.2\ unit`

Therefore the Segment DF is 7.2 unit.