In the given figure E is the mid-point of XY and EF∥YZ. If XZ = 7 cm then find XF.
Answers
Answered by
0
Answer:
Consider △ADB and △EDF,
∠ADB=∠EDF [ Vertical angles ]
∠ABD=∠FED [ Alternate angles ]
∠BAD=∠EFD [ Alternate angles ]
∴ △ADB∼△EDF [ By ASA criterion ]
⇒
DE
BD
=
FE
AB
⇒
y
4
=
10
6
⇒ 6y=40
⇒ y=
6
40
=
3
20
⇒ y=6.67cm
Similarly, △ADE∼△CDE [ AA criterion ]
⇒
BE
DE
=
BA
DC
⇒
10.67
6.67
=
6
x
⇒ x=6×
10.67
6.67
⇒ x=3.75cm
∴ The values of x and y are 3.75cm and
6.67cm.
Similar questions