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
[tex]\dfrac{BD}{DF}=\dfrac{AC}{CE}[/tex]
Substituting the values we get
[tex]\dfrac{12}{DF}=\dfrac{10}{6}\\\\DE=\dfrac{72}{10}=7.2\ unit\\\\DF = 7.2\ unit[/tex]
Therefore the Segment DF is 7.2 unit.