Question

Point D and E are the points on sides AB and AC such that AB = 5.6
, AD = 1.4 , AC = 7.2 and AE = 1.8 . Show that DE || BC

Answer 1

Answer:

We have 

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.∴       BD=AB−AD=(5.6−1.4) cm=4.2 cm

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.∴       BD=AB−AD=(5.6−1.4) cm=4.2 cmand ,

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.∴       BD=AB−AD=(5.6−1.4) cm=4.2 cmand ,EC=AC−AE=(7.2−1.8)cm=5.4cm

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.∴       BD=AB−AD=(5.6−1.4) cm=4.2 cmand ,EC=AC−AE=(7.2−1.8)cm=5.4cmNow,    DBAD=4.21.4=31 and ECAE=5.41.8=31

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.∴       BD=AB−AD=(5.6−1.4) cm=4.2 cmand ,EC=AC−AE=(7.2−1.8)cm=5.4cmNow,    DBAD=4.21.4=31 and ECAE=5.41.8=31⇒         DBAD=ECAE

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.∴       BD=AB−AD=(5.6−1.4) cm=4.2 cmand ,EC=AC−AE=(7.2−1.8)cm=5.4cmNow,    DBAD=4.21.4=31 and ECAE=5.41.8=31⇒         DBAD=ECAEThus, DE divides sides AB and AC of △ABC in the same ratio.

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.∴       BD=AB−AD=(5.6−1.4) cm=4.2 cmand ,EC=AC−AE=(7.2−1.8)cm=5.4cmNow,    DBAD=4.21.4=31 and ECAE=5.41.8=31⇒         DBAD=ECAEThus, DE divides sides AB and AC of △ABC in the same ratio.Therefore, by the converse of Basic Pro-portionality Theorem, we have

We have AB=5.6cm,AD=1.4cm,AC=7.2cm and AE=1.8cm.∴       BD=AB−AD=(5.6−1.4) cm=4.2 cmand ,EC=AC−AE=(7.2−1.8)cm=5.4cmNow,    DBAD=4.21.4=31 and ECAE=5.41.8=31⇒         DBAD=ECAEThus, DE divides sides AB and AC of △ABC in the same ratio.Therefore, by the converse of Basic Pro-portionality Theorem, we have                  DE∣∣BC