Question

In the figure AB, CD, and EF are parallel lines. PC 4 cm, CE 2 cm, PD 6 cm. Find DF and PF​

Answer 1

Answer:

In △BCD and △BEF,

∠DBC=∠FBE (Common angle)

∠BCD=∠BEF (Corresponding angles of parallel lines CD and EF)

∠BDC=∠BFE (Corresponding angles of parallel lines CD and EF)

Thus, △BCD∼△BEF (AAA rule)

Hence,

BE

BC

=

BF

BD

=

EF

CD

(Corresponding sides)

x+3

x

=

BF

BD

=

4.5

y

..(I)

Similarly, △FCD∼△FAB

Thus,

FA

FC

=

AB

CD

=

FB

FD

7.5

y

=

BF

DF

(II)

From I and II,

BD=

4.5

y

BF and DF=

7.5

y

BF

BD+DF=BF

4.5

y

BF+

7.5

y

BF=BF

7.5y+4.5y=7.5×4.5

y=

16

45

Also,

x+3

x

=

4.5

y

x+3

x

=

16×4.5

45

x+3

x

=

72

45

72x=45x+135

27x=135

x=5cm