Question

In 𝐴𝐵𝐶, 𝐴𝐸 = 12 𝑐𝑚, 𝐴𝐶 = 20 𝑐𝑚, 𝐴𝐵 = 25 𝑐𝑚, 𝐵𝐷 =10 𝑐𝑚.
State whether line 𝐷𝐸 is parallel to side 𝐵𝐶. Give reason.

Answer 1

Given In △ABC, 𝐴𝐸 = 12 𝑐𝑚, 𝐴𝐶 = 20 𝑐𝑚, 𝐴𝐵 = 25 𝑐𝑚, 𝐵𝐷 = 10 𝑐𝑚.
Now, in triangle ABC, we have
AD = AB − BD = 25 − 10 = 15 cm.

$\frac{AD}{AB}=\frac{15}{25}=\frac{3}{5}$
$\frac{AE}{AC}=\frac{12}{20}$
$\frac{AD}{AB}=\frac{AE}{AC}$
So,
By converse of BPT theorem,
DE || BC.