Question

prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side (using Converse of basic proportionality theorem​

Answer 1

Answer:

★ Basic proportionality theorem

If a line is drawn parallel to one side of a triangle to intersect the other two side interesting points than the other two sides are divided in the same ratio and  this theorem is also known as Thales theorem.

★ Converse of basic proportionality theorem

If a line divides any two sides of a triangle in the same ratio then the line must parallel to the third side.

Given:

ΔABC in which D and E are the mid points of AB and AC respectively such that AD=BD and AE=EC.

To Prove: DE || BC

Proof: D is the mid point of AB (Given)

∴ AD=DB

⇒ AD/BD = 1 … (i)

Also, E is the mid-point of AC (Given)

∴ AE=EC

⇒AE/EC = 1 [From equation (i)]

From equation (i) and (ii), we get

AD/BD = AE/EC

∴ DE || BC [By converse of Basic Proportionality Theorem]

Hence , the line joining the mid points of any two sides of a triangle is parallel to the third side

Answer 2

Answer:

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