Question

Find segment DF. Picture will help you.

Answer 1

Answer:

Therefore the Segment DF is 7.2 unit.

Step-by-step 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

$\dfrac{BD}{DF}=\dfrac{AC}{CE}$

Substituting the values we get

$\dfrac{12}{DF}=\dfrac{10}{6}\\\\DE=\dfrac{72}{10}=7.2\ unit\\\\DF = 7.2\ unit$

Therefore the Segment DF is 7.2 unit.