Question

Assertion (A): In a ∆ABC,D and E are points on sides AB and AC respectively such that BD = CE. If <B= <C, then DE is not parallel to BC.

Reason (R): If a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side.​

Answer 1

Answer:

assertion is false but reason is true because accourding to thale theorem if a line divide any two side of a triangle in same ratio then the line must be parallel to third side.

Answer 2

After reading the statements of assertion and reason we can conclude:

The Assertion(A) is false and Reason(R) is correct.

• The reason R states that if a line divides any two sides of a triangle in the same ratio, then the line must be parallel to the third side. This theorem is known as the Basic Proportionality theorem.
• The assertion can be proven by the converse of the Basic Proportionality theorem, therefore the statement is false.

The proof for assertion A:

In ΔABC, we have

∠B = ∠C

Then we can say that,

⇒AC = AB (As when the angles are equal the sides corresponding to it are equal)

⇒ AB = AC (Sides that are opposite to equal angles are equal)

⇒ AD + DB = AE + EC

It is given that, BD = CE then,

⇒ AD = AE

We have got AD = AE and BD = CE

⇒$\frac{AD}{BD}=\frac{AE}{BE}$

By converse of BPT, DE ║ BC