Question

All the students i am challenging you if you can then do this

Prove that the line joining the midpoints of any two sides of a triangle is parallel to the third side by using the converse of basic proportionality theorem.

Answer 1

Answer:

Here is your answer

                                                             

From the triangle PQR in which ST are the midpoints of PQ and PR respectively such that PS = SQ and PT= TR

To prove: ST ǁ QR

Proof: S is the midpoint of PQ (Given)

Therefore, PS = SQ

=>PS/QS = 1 – – – – – – – – – (1)

Also, T is the midpoint of PR (Given)

Therefore, PT= TR

=>PT/TR = 1 [from equation (1)]

From equation (1) and (2) we get,

PS/ QS = PT/ TR

Hence, ST ǁ QR [By the converse of the basic proportionality theorem]

                                                                                                                             

Answer 2

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.

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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....