Question

In $\Delta$ABC and $\Delta$DEF, AB$=$DE, AB$||$DE, BC$=$EF and BC$||$EF. Vertices A, B and C are joined to vertices D, E and F respectively. Show that AD$||$CF and AD$=$CF.

Answer 1

Given $AB=DE$ and $AB\parallel DE$

Thus, by property of parallelogram, ABED is a parallelogram.

∴ AD = BE
AD || BE ………. (i)

Similarly, $BC=EF$ and $BC\parallel EF$

Thus, by property of parallelogram, BEFC is a parallelogram.
∴ CF = BE
CF || BE ……………. (ii)

Comparing (i) and (ii), we can write,
$AD=CF$ and $AD\parallel CF$