Question

In triangle ABC,D and Eare point on AB and AC respectively If AB=5.6cm,AD=1.4cm,AC=7.2cm,AE=1.8cm, determine whether DE is parallel to BC or not

Answer 1

Given : AB=5.6cm,AD=1.4cm,AC=7.2cm,AE=1.8cm

To find : DE is parallel to BC or not

Solution:

AB=5.6cm, AD=1.4cm, AC=7.2cm, AE=1.8cm

thus

DB = AB - AD

DB = 5.6 - 1.4

DB = 4.2 cm

similarly

EC = AC -AE

EC = 7.2 - 1.8

EC = 5.4 cm

now ,

$\frac{AD}{BD}=\frac{1.4}{4.2}=\frac{1}{3}\\\\\frac{AE}{EC}=\frac{1.8}{5.4}=\frac{1}{3}$

THUS , DE divides the side AB and AC of the triangle ABC in the same ratio

therefore ,

BY the converse of the BPT theorem

DE parallel to BC

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Answer 2

Step-by-step explanation:

Given : AB=5.6cm,AD=1.4cm,AC=7.2cm,AE=1.8cm

To find : DE is parallel to BC or not

Solution:

AB=5.6cm, AD=1.4cm, AC=7.2cm, AE=1.8cm

thus

DB = AB - AD

DB = 5.6 - 1.4

DB = 4.2 cm

similarly

EC = AC -AE

EC = 7.2 - 1.8

EC = 5.4 cm

now ,

\begin{gathered}\frac{AD}{BD}=\frac{1.4}{4.2}=\frac{1}{3}\\\\\frac{AE}{EC}=\frac{1.8}{5.4}=\frac{1}{3}\end{gathered}

BD

AD

=

4.2

1.4

=

3

1

EC

AE

=

5.4

1.8

=

3

1

THUS , DE divides the side AB and AC of the triangle ABC in the same ratio

therefore ,

BY the converse of the BPT theorem

DE parallel to BC