Question

In the given figure, AD = 2cm, BD = 3 cm, AE = 3.5 cm and AC = 7 cm. Is DE parallel to BC ?
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Answer 1

Answer:

No

Step-by-step explanation:

As B.P.T Basic proportionality theorem

if AD/BD=AE/EC Then only we can say that DE//BC

But here,

AD is 2cm, BD is 3 cm

AC = AE+EC

AE= 3.5cm

AC= 7 cm

put the respective values of AC and AE we have,

7 cm = 3.5cm+ EC

EC = 3.5 cm (by solving the above eqn)

so, AD/BD= 2/3

AND

AE/EC= 3.5/3.5

AE/EC= 1/1

AS PER B.P.T

AD/BD must be equal to AE/EC

BUT this condition is not fulfilled by the given values.

So, DE is not // to BC.

Answer 2

DE is not parallel to BC.

Given: Measurement of AD, BD, AE, and AC.

To find: Parallelism of two triangles.

Step-by-step explanation:

• The triangle is correct if the circumcircle's center is on the triangle, and the hypotenuse's circumcircle's center is on the hypotenuse.

• The inverse of Thales' theorem is that the center of a right triangle's circumcircle sits on the hypotenuse.

Solution:

$EC=AC-AE = (7 - 3.5)$ cm

= $3.5$ cm

$\frac{AD}{BD}=\frac{2}{3} and \frac{AE}{EC}=\frac{3.5}{3.5}=1$

So, $\frac{AD}{BD}$∉$\frac{AE}{EC}$

Hence, DE is not parallel to BC, according to Thale's Theorem.