Question

Please help me with these questions.​

Answer 1

Mid point Theorem :

The line segment joining the mid points of any two sides of a triangle is parallel to the third side.

Given :

A ∆ ABC in which D and E are the mid points of AB and AC, respectively.

To prove :

DE ∥ BC.

Proof :

Since D and E are the mid points of AB and AC, respectively, we have AD = DB and AE = EC.

Therefore,

$\dfrac{AD}{DB} = \dfrac{AE}{EC}$

Therefore, by the converse of thales theorem, DE ∥ BC.

Answer 2

Mid point Theorem :

The line segment joining the mid points of any two sides of a triangle is parallel to the third side.

Given :

A ∆ ABC in which D and E are the mid points of AB and AC, respectively.

To prove :

DE ∥ BC.

Proof :

Since D and E are the mid points of AB and AC, respectively, we have AD = DB and AE = EC.

Therefore,

\dfrac{AD}{DB} = \dfrac{AE}{EC}

DB

AD

=

EC

AE

Therefore, by the converse of thales theorem, DE ∥ BC.