Q

# In ∆ ABC and ∆ DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that (iii) AD || CF and AD = CF

Q : 11        In $\small \Delta ABC$ and $\small \Delta DEF$, $\small AB=DE,AB\parallel DE,BC=EF$ and $\small BC\parallel EF$. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. $\small 8.22$). Show that

(iii) $\small AD\parallel CF$ and $\small AD=CF$

Views

To prove : $\small AD\parallel CF$ and $\small AD=CF$

Proof :

In ABED,

In BEFC,

BE=CF.................3(BEFC is a parallelogram)

BE||CF .................4(BEFC is a parallelogram)

From 2 and 4 , we get

From 1 and 3, we get